There is one crucial problem with your suggestion: what would be the advantage of a bigger faction? Army, money, magic... but not research? Why is research so special, and not, for example, trade? If you really want to make a bigger faction more 'expensive' (i.e., restricted in growing exponentially in power), than you have to introduce a reasonable mechanic to support these restrictions. Think about upkeep. You can produce units as fast as you can (as you are a ruler of a mighty empire), but you still have to pay your units, so there is a reasonable factor that limit your expansion. In your proposal there is lack of such mechanism, and more importantly: why research, and not anything else?
Research is special because it improve all the other aspect of the strength of an empire. As an example, let's use military strength. Without research scalling, the bigger empire will have (sometimes much) better units. But since its infrastructure would also be bigger (more cities), it will end up with both better units and more of them. So it gets both a quality and a quantity advantage from being bigger. Using research scaling is (in my eyes) the ideal way to prevent the quality bonus, while letting them retain the quantity bonus.
There are other ways to restrict an overeager expansion. For example the essence mechanic in Elemental, or the corruption in Civ1-3. But these are short term solutions, while the long term research advantage remain.
Let's assume that, despite my feelings, we try to develop a 'limiting game mechanic' into the game which would prevent big empires to gain to much technological advantage. Easiest way is to introduce diminishing returns. This way we would easily limit big factions by implementing a mechanism which would be described as 'the more money you give to your scientists, the more will be wasted, due to inefficient management'. Although easy, this solution has one big disadvantage: there won't be any reason to build more and more research centers. If we were to introduce this mechanic to most of game elements, than there would be virtually no reason to grow larger, as there wouldn't be any things to spend your money on.
Second way out (which I find much more balanced) is to make the player pay for their universities. Think about GalCivII; you build more science labs - fine, but remember that they cost money. This would be a typical solution, but it's not that interesting to make everything so cliche. Sure, we can make everything have it's upkeep value, but in the end we would create the same thing which I described before - a game where advantages of bigger empire would be basically nullified by series of game balancing elements.
Diminishing returns are not going to change anything. They will affect small specialised researchers as much as big empires. And the main effect will be to smoothen everything toward the middle. But the one with the advantage will remain the same. As for making players pay for the universities, that's no different, as bigger empires have bigger ressources anyway. And GalCivII is an horrible example, research-wise. Do you remember once fighting a small enemy with decent techs? Minor civs were horribly nerfed due to that effect, and it made fast expanders (Torian/Thalan) all the more powerful.
I don't know what were your motives of writing this proposal, but you have to understand that being bigger (and stronger) isn't without it's cost - even if you drop the heavily limiting mechanics. First, the bigger the empire, the longer the borders, thus more land to protect. Second, being stronger makes people afraid of you, hence people start to team up against you (which wouldn't be a case if you were sitting quietly in your corner). Third, upkeep of your army devours large portion of your income. Forth, bigger kingdom means more occasions to make mistakes, which might cost you dearly. There are several other factors that make the big empire hard to rule, so if you really feel that a strong faction should be limited in terms of research (or the small one should get some bonuses) then think carefully: why should it be penalized, and how to make it work in the game.
I don't think any of these examples are arguments why bigger empires are costly. First, your armies size are going to grow with the territory you possess, but the borders will only grows as the square root of that territory size. Simply put, the bigger your blob, the more you have inner cities who are very far from your borders and whose troops can be sent to the front. Same for the upkeep, since your income increases with your size. As for mistakes, yes you have more occasions for mistakes, but you are also more in a position to survive them (what's loosing a city to some rebels when you have a hundred of them?).
But that paragraph makes me think of why you dislike my proposal : you think of it as a way to penalize big empires. This isn't the case : it is a way to prevent big empires from being too much advantaged by their size. A properly design scaling system should have both small and big empires research at about the same pace, with differences depending on economical, infrastrural or cultural (faction bonus) reasons.
Why I somewhat dislike its research system, EU3 is a good example of a game with research scaling. The more provinces you have, the more money needs to be invested to get the next technological breakthroughs. As a result, you get 1 or 2 provinces minors (like Switzerland) have about the same tech levels as huge countries (like France).