It's easy to solve, just not in a way that most players will agree to. Because most players want to see this happening to others - not to themselves. Then the game/devs are just punishing them.
One way to make expansion harder is to make conquering new lands somewhat counter-productive.
One thing I'd like to see taken into consideration is when the technologically advanced player snaps up vast tracks of the world where people lived in mud huts. I see the risk of making this Vicky-lite, but I think players would accept the fact that grabbing "backward" parts of the world would have an adverse effect on tech progress by adding other costs, or reducing the effectiveness of tech spending. For example, how could someplace become a "core", and the equal to all the other possessions of a country, if people were still living in their mud huts? To advance your possessions you should have to expend money which might have otherwise pushed you further along in the tech race.
Imagine a player country consisting of one rich province in Europe and hundreds of captured provinces (not colonies) in poor parts of the world? Why is that country a technologically advanced one, just because it started in Europe? Fifty years later I make European-quality soldiers out of primitive tribesmen with no cost or effort? It's not game breaking, we've been doing it all along, but I think people would accept a different way of handling this. Granted, this is not the same slowing mechanism that the OP was talking about, or the same challenge, but if we're talking generally about how to limit the player's growth in ways that people will accept as legitimate, slowing tech progress when you capture low-tech provinces would seem to work for me.
As for the OP's idea, perhaps there could be an event series which permitted the player to go down that road if that's the challenge he wanted. One branch perhaps offers the player greater control over his leaders, but with the declining country trouble the OP described (the other branch goes down the normal path). Giving me a list of twenty potential rulers might make it worth dealing with a declining country if that's what I was in the mood for, and a country in decline would have stability problems which could easily explain how any one of twenty people could have taken charge. If I'm the source of quasi-revolutionary upheavals, it also prods my neighbors to attack. Some players view the EU civil war event as a challenging bit of fun. Most I think viewed it as the game randomly hitting them with a frying pan ("I think this game of solitaire would be more challenging if I stabbed myself with a fork!").
Make it an option, complete with with tempting gameplay bonuses, and I think everyone would be happy.