Charles, I've attacked a simple save file as an example of how trucks rally passengers. There are a series of German trucks on the road and the lead truck has a suppression of 6 and the passenger has a suppression of 7. You can unload the passenger and confirm this. Reload the file and rally the truck with the passenger still on board. It might take a reload or two because the experience and morale of the truck is just national average. Once you do get a successful rally, unload the passenger as well and you will see it also rallied. This method allows you to see both the before and after pictures of the situation. I'm not sure if it should work this way, but it does.
As far as ammo trucks running away, it is something that can happen, but isn't common. Since ammo trucks are unarmored, they are more likely to be destroyed or immobilized than just suppressed. I have had them run before, but the overall objective is to keep ammo trucks out of harms way whether they are core or support. Typically, I'm careful with my supply vehicles, but the AI sometimes just slings artillery randomly and gets lucky. I start with trucks, but switch to armored carriers as soon as practical. Some nations have armed and armored ammo supply vehicles available and some don't. Armed isn't as important to me since their role isn't to fight. I use two supply vehicles as battalion level support with my core.
Your theory about deleting units from my core is incorrect because you don't find out what the mission is until after you pass the repair phase. I've just tried out different units in my core to see if they worked for me and what I wanted to achieve. One example is I had added some Elefants and just found out they weren't worth it. Too expensive and I just figured I didn't need a slow moving pillbox. There are other instances where I had towed artillery with transport. I upgraded them to SPAs. As such, I didn't need the transports anymore and deleted them. Mostly, I add units to my core which is at 125 at the moment.
My core actually has 28 SdKfz 251/1 half-tracks for transport and an additional 8 recon or assault tracks. The transport tracks average 1 kill each, which isn't much but I use them to pepper a target and then run up and unload my infantry. Most of the time in those assaults, the infantry gets the kill. Trucks, even the few that are armed, aren't good for this type of attack. The tracks are with my core at all times. Most of my battles aren't defends so they are useful in delays, meeting engagements, advances and assaults. When the mission is a defend, I do park them but make a nice ad-hoc reserve if I need to use them as such. Personally, I find it a good thing if they can just stay parked the whole battle because it means I didn't need them.
On to the speed aspect, I do consider it to be important to not be in the same place for any length of time. This goes back to the artillery aspect again. The objective is to get out of the impact zone as soon as possible. Usually not a problem with trucks because if they don't blow up when the artillery comes in, they drop their load and cease to be transports. Tracks are much more survivable in this area. If I have units in any given area for more than three turns, I feel artillery is a risk. Being able to move and move quickly takes that out of the picture. Being able to move fast doesn't translate into being careless. The main purpose is to get them to from the LD to their assault position as quickly as possible so time. Sometimes, that assault position is in the enemy rear area. Why go through what you can go around?
My entire force ends up in the enemy rear. No assets are left behind. I find it amusing to see the AI "counter-attack" and push into my deployment zone to find nothing there.
I am getting what you are saying about trucks in the core, but am just saying they aren't entirely worthless. Nearly so, but not completely. There are a couple of points in favor of it and at least six against. The point I was arguing against is that there were no benefits what so ever. As I said, I am not a fan of trucks unless it's the enemy using them. They die easily, unload at the slightest amount of incoming fire, they rarely have any offensive or defensive capability, off road mobility is limited, get stuck easily, etc. Because of these limitations, half-tracks are always the better option. I will take a track over a truck every time.
My core is two SS infantry companies, one tanks company, two heavy tank sections, a couple of SPA batteries, recon elements, two SPAA sections, three MG-42 sections and one section of ammo supply tracks. Of my core, only my two ammo supply tracks are unarmed. This force is balanced well to deal with most missions. This core runs about 8,000 points, mainly due to their experience. I've cycled different units in and out over time. The Elefants I mentioned earlier didn't meet my needs. I had StuGs at one point too, but I replaced them with Tigers. The 88mm on the Tigers is good, but I was more interested in the larger ammo supply the Tigers had. I've fought battles where I was running out of ammo and even having resupply didn't help. There wasn't time to pull units off the line for resupply. PzKw IVh tanks were hitting AI armor and half-tracks with HE rounds! Terrain prevented easy shifting of units from one section to another and visibility was low enough that units from one flank couldn't fire across the front of the other. The AI had a combination of 240+ AFVs and half-tracks, about 180 were left burning. My core is more oriented toward offensive action. It use to have six towed ATGs, but I got rid of those as well, because I found them generally useless in this role. My support points can be used to buy ATGs if the battle calls for them. I also found having any non-mobile units in my core was a waste as the AI tends to have scads of artillery with nothing better to do than pound them. Those are actually what were replaced by the Elefants. The campaign is in Italy right now and I don't encounter anything the Tigers can't deal with so the Elefants are gone also.
Because of the size of my core, I do rely heavily on defensive obstacles in defend missions. The AI usually attacks with 25,000+ points and I now have only 23 tank killing guns. Obstacles are required to give those 23 guns time to engage targets. Using obstacles isn't that great of an advantage because the AI is very adept at getting through them somewhere and often everywhere. I've faced situations where I've been out numbered 8 to 1 on tanks and time is required to thin them out before they get to me. A mobile defense doesn't make much sense, being that you would be giving up one bonus to being on the defense, the revetment for your tank. Aside from mines, I use fire trenches, wire and dragon's teeth. Other points go for bunkers and artillery. In a defend, very few support units are at the broken end of the bottle. Mostly my core is on the line. The only exception are the bunkers, which have a rifle. My infantry stays hunkered down in those for protection against incoming artillery until they have to deploy against the AI assault force. As mentioned, my tracks all stay back on this type of mission, but there is one thing to consider. Each of those parked half-tracks have a AAMG so they provide support, even when off the line. They have taken out enemy aircraft before. As for aircraft, I rarely use them, except the spotter. Battle field intelligence is more valuable than the few units that a strike unit could take out.
Trust me, my core does most of the fighting. With a core of 8,000 points and support points ranging from 500-2,000 points, I couldn't win if they didn't. My force is designed as a reasonably realistic battalion sized task force oriented to the offense. As such, the SS infantry companies have track transport. I could go without tracks, but it doesn't make sense with the model I'm using. For me, putting them riding tanks isn't an option because I don't think it is modeled well in the game. Tank riders should be more vulnerable to casualties than they really are in the game, IMO. Overall, my core has served me well. There are instances where support units go in first. My core isn't an engineer battalion. I've got a few, but not enough to effectively breach the enemy line on an assault. They make the hole and my core blasts through it. My engineers are more intended for mines encountered beyond the main line. Remaining points tend to go for artillery, air spotter if available, additional recon and to fill any gaps that need filled, if the mission is something other than an assault. My standard on delays is six MG-42s and six 50mm ATGs. At a 2 to 1 disadvantage, I typically need more tank killing guns and the 50mm works well against the Americans and British in 1943. There are some DARs I've done out there that detail how my battles have gone.