It's supposed to be a trade-off. It's mostly a balance thing. Otherwise, with the monarch power system, which I think is fundamentally a good idea, buildings and tech would only create a positive feedback loop, a rich get richer sort of scenario.
You sort of hit the nail on the head yourself, inadvertently.
You're simply not supposed to be able to keep up in buildings, tech and expand at the same time.
I know that - it was just a counter argument to your "If you get a bad monarch, you will simply have to choose what to prioritize,", but looking back at it, it probably could've been worded better.
There wouldn't really be any loop though, considering that there's only one building (that you can only build one of) that actually helps tech directly. You can get buildings that give you more papal influence, which in turn increases your chance to control cardinals and reduce tech cost though - but not by very much. I understand completely that it's a balance thing, and that balance is vital in games like this, I just think it could've been done differently. In CK2 you can actually boost your tech-increase with buildings, and as far as I know that works quite well - but the techs aren't as vital as the ones in EU4, of course. For me, upping the cost to core, increasing the cost to spread your culture and keeping that balance that way would make a lot more sense. Like you say, I can see why they've made it the way it is, I just think it's a bit of the easy option and not realistic at all. Pretty much everything else about the game is spot on for me.
Out of curiosity, which nations have you played with so far? I started out with the usual easy game with Denmark (to get used to the game - as I said, I haven't played EU3, so a lot of new stuff for me) and took over most of the world (apart from large chunks of Asia) before getting bored. Playing a game with Austria at the moment and just managed to recreate the HRE. Might try doing the same with a smaller nation at some point.
I've got to say I haven't really understood the new trade system yet. You can either place a merchant in a trade node or have him divert trade? But to where? A random one within reach that you control? You send smaller ships to control each trade node which helps with tarifs, but also forwarding trade to nodes you control? Seems impossible to have a lot of power in all the nodes from Asia all the way back to Europe which I read you should be doing.. Maybe I have this part wrong.
If you transfer trade you can select the direction from the trade-map (assuming it goes in more than one direction of course) and it then gets added to the trade value at the next node. From there it can either be transferred further or be collected - in the end, you can have trade from Asia going all the way around Africa, to the eastern coast of America and then to Europe before it's collected. If you look a trade note you can hover the values and see where your trade power is coming from. You can get it from simply having provinces (certain provinces has a special modifier as well), buildings and protecting the trade note with your boats. It's a great aspect of the game and once you get the hang of it, it's actually quite simple - took me a while before I really understood it as well though
Collecting from trade in a node where your capital isn't placed will give you a huge trade power penalty, but in certain cases it might be worth it anyway. Feel free to post more questions if you've got any - otherwise checking out youtube or a wiki is a good way to gain some understanding as well.