A lot of the "chartered accountancy" school of wargamers bow down and worship at the holy altar of TO&E charts. "So it was written, and so it must have been".
The reality is that these things are about as accurate as modern organisational charts in businesses. (See if you can find the org chart for your organisation

!. They reflect the
management's view point of how things should be, and do not necessarily reflect the on-the-ground "shop floor"
actuality. Civilian organisations have absenteeism due to sickness and so on, military units have the same plus battle casualties, both to "plant" as well as staff.
And in both, the "middle management" (batallion, company and even higher) will often make local "tweaks" to make the organisations work "at the coal face" level, without necessarily bothering the top-level beurocrats. They may hire contract staff if this is a way to get more people and the money comes from a different budget than "staff", and look at how the original microcomputers came in on "office equipment" budgets, without the top levels knowing about this, and without the centralised IT departments knowing that so much strategic company IT work was now being done locally in departments on Visicalc, with no IT department overview or QA of the code. same thing in our TA rifle company - we often borrowed the next door engineer coy's BRENS on a tactical weekend, if they were off building bridges. Or they would "lend" us a few guys who needed infantry tactical brush-up training, so we would then be a bit overstrength.
Some nationalities are more rigid as to this sort of thing and apply "doctrines" which all have to obey. Others, like the British are more flexible, and leave minor details up to the colonel of the batallion to adjust as he sees fit.
So a wargamer comes from the beurocratic worship of TO&E charts, and assumes things are as the chart, unless he actually spends some time reading some history on the subject. (It also helps if he has been involved in some sort of corporate organisation, whether military or civilian, so he can put a reasonable skepticism on such things as org charts in the first place!

.
So a wargamer willl make such statements as "All WW2 UK infantry batallions had a carrier platoon for scouting". But history shows that most batallions actually broke these units up, as they had better use for the manpower elsewhere, and the carriers and drivers would be used as "tin jeeps" to do things like drive the RSM around on his rounds, deliver hot meals ammo and mail to the front etc.
A Wargamer will make a statement from TO&E that "a UK rifle platoon had a 2 inch mortar at platoon HQ, as well as a Boyes ATR". Well,
my batallion had 2 inch mortars issued, but these stayed in the armoury, as we had better use for the 2 men supposed to carry the silly thing about. And in WW2, the Boyes was determined to be useless by many units, and was conveniently "lost". Again, freeing up manpower which is always a shortage in rifle platoons even in peacetime (there is usually 2 or 3 men away on courses, before we get to those off sick or on leave etc) let alone wartime casualties (where you add dead and injured to the same amounts off sick, on leave, or on courses etc as in peacetime, probably
more off on courses in war!

).
Really useful (tm) items of course did not get lost. if a rifle platoon shrank due to losses, the 3 brens would be kept, even if rifle srength shrank. Any rifle platoon worth its salt would of course try to "aquire" any really useful(tm) items that others had not nailed down, own-side or OPFOR.
One US Division in NW Europe deliberately stockpiled and issued as regular stores any captured german panzerfaust they came across. (I may well add a rifle squad with pfaust if it is not there already)
The Soviets did the same - regularly using panzerfausts, and also adding nebelwerfers to MRL units for example on and add-hoc basis outside TO&E charts so long as the ammo supply held out. There are Soviet units with captured pfaust.
So remember at all times that a TO&E chart is just a "management level ideal", just like any departmental or divisional civilian org chart. It is a starter, but must be modified by any historical research. A useful starter though - as wargamers are the sort to take a little historical "nugget" and then try to apply that to thier entire army. This is a known fact from ancient wargames to modern. The Romans used bolt throwers mounted on carts on one or 2 occasions in the field, and so about a third of Roman armies on the wargames table usually have cart mounted bolt-throwers trundling around..
So we
do need to restrict the gamers choice somehow, and a TO&E chart is useful for this, but equally it cannot be treated as absolute "law" just because it is written down on paper by a beurocrat in the "human resources" department.
Cheers
Andy