Generally, I don't like the idea. (Sorry.) It doesn't seem realistic to me, and I don't like artificial restrictions. The current system does seem realistic, in that you are restricted from researching everything due to economic factors, rather than someone else's arbitrary choices. Makes for more variety.
However, I would be in favor of increasing research costs overall, and then giving discounts to players who are specializing in an area. For instance, if you've got two physics techs already, then the third one would be easier to research. Or maybe divide techs into categories like offensive, defensive, and infrastructure. This would encourage specialization without requiring it. Also it would make trade more interesting, because you wouldn't necessarily know how much each tech cost each player.
Or maybe research labs should be specialized. That would be more realistic. A bio lab isn't going to discover shields, and a physics lab isn't going to discover plague bombs. Or perhaps specialized labs should just get a bonus over general research facilities for certain techs, but a penalty for all other techs. So then the player has to decide what kind of labs to build. Think of what that would do for trading and strategy.
Also, I would like to see more incremental advances. "Hmmm...should I research more powerful weapons or longer-ranged ones or easier aiming or faster reloading or less supply usage or cheaper build/maintain cost?" Again, more strategy.
Lastly, there should be more techs. This would also encourage player-initiated specialization. (Because there would be too many techs to research them all.) Biology, in particular, needs to be fleshed out. (Sorry, couldn't resist that one.
) Where is genetic engineering?