In general I really like the idea that tech should be linked to trade. Also it would really be nice if they did like you say and make it so that different countries require different approaches to tech advancement.
However I hate the idea that the state should have a "research budget". It's such a terrible meme, something they invented for the Civ games and that stuck ever since. A simulationist game like EU should not have this.
I mean, what is this supposed to represent? Kings and princes did not finance research academies in any of those times. They financed all kinds of stuff - administration, clerics, the military, some welfare, occasionally also business ventures proposed by private individuals - but not research academies. Research happened "on the side", it was something to which people devoted their time when there was a need for it and when circumstances were right.
I don't like the idea that there should be a "research slider" which you push as far to the right as possible, to reach an arbitrary threshold of arbitrarily defined research points. I much prefer the CK2 system where advanced still happen in small steps, but based on random chances, not on sliders and research point counts. You still have a sort of idea how far you are from a breakthrough, but you cannot really time it. You can tell if you are stagnating, you can tell if you are in the lead, but you can't say "this is my current rate of progress, and we will discover this tech seven years, five months and ten days from now, at half past six in the morning". I always hated this about EU3, it's a fun game in many ways, but in so many other ways it degenerates into bean counting.
Playing a game like EU is, to me, about putting you into the position of a statesman - about immersion. If you play the Incas and you want gunpowder, well, think for a second about how the Inca High King would go about this, and then do that! Tell the scribes and priests to go out of their way to record everything there is to know about the foreigners and their way of doing things. Think about how you can get a closer view at their stuff. Without letting them know how backwards and weak you really are. Make a choice about whether it's better to pull their traders into your country, and try to learn from them, or to close yourself off, keep the Spanish out and try to find out about their stuff in other ways (Equip expeditions to find their settlements, and those of other Europeans before they find yours... raid them... or turn your realm into a hermit kingdom, and limit their trade to specific places, like Deshima...) And then hope that this brings you success, as soon as possible. It should not be about shoving some sliders to the right, and then twiddling your thumbs while you watch the progress bar creep up slowly.
I mean, COME ON! In Eu3 tech research is less interesting and less immersive than watching your computer burn a DVD.

Do something about it, Paradox!