The root of the problem is, perhaps, the fact that EU4 misrepresents standing armies so badly, in that everybody has them from the start. If standing armies were a thing that only develops during the game and that are actually really hard to afford, they would be a perfect money sink. However, such a fundamental change - which would probably require the introduction of feudal levies - is unlikely to be introduced at this stage of development of EU4.
The problem that there is so much money in the game that the economical side of the game becomes almost irrelevant after a certain point remains though. Which is bad, because it makes all strategic choices related to economics (the trade idea group, religions - like the newly introduced anglicanism - which grant mostly economic benefits...) underpowered.
My idea would be to tie troop maintenance to your level of army professionalism. High army professionalism represents your military to actually be a standing army, and thus maintenance would be much higher. In turn, with low army professionalism and thus lower maintenance, your ingame armies could represent only the means to actually field an irregular force the size of your actual ingame army. Apart from that, I'd like to see army maintenance raised across the board. Prolonged warfare should almost always force you to take up loans at some point, as it was in reality. This would also indirectly tackle the absurd power creep and blobbing that occurs even for medium powers.
Given the sheer amount of excess gold one has access to from the midgame onward, this would of course only be part of the solution. More mechanics to cut the ridiculous inflation are needed.
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