Hence the anti-revolutionary power block will break apart in 1-2 wars.
Maybe it will, maybe it won't. I think this scenario can be situational enough that it doesn't have to happen one certain way every time you play a game. Also if you can help other revolutions as a revolutionary country, I imagine others can intervene on the absolutist side as well. If everyone is dealing with revolutions at the same time (meaning everyone is busy), the first 1 or 2 countries that can resolve their situations could be the dealbreaker for the others (if they have the strength and will to intervene for others in the aftermath).
If it is RNG for the revolution to take hold (and nations flipping republic so easily is btw a-historical through and through), then it is an even worse idea. So I have to go through a massive war to maybe get a country to like me. Why bother going revolutionary in the first place then?
Since so far we don't know anything about how revolutions will work and what is the benefit of going revolutionary, then this conversation is about something that is right now hypothetical, but my guesses to your question are:
-It could give you situational benefits if it fits your playstyle (like new laws, new diplomatic options, new espionage options, different parliament, etc.)
-Roleplay
-If you fail to stop the revolution in your country but doesn't want to start a new game, it could be a challenge (also fun) to adapt to the new situation and try to make the most of it
-Doesn't necessarily have to be a massive war to support a revolution, it could be only monetary contribution, I mentioned it because of the discussion in the second page about supporting rebellions....but yeah, why not? If you are the first one to flip revolutionary, you are probably desperate for allies, IF being revolutionary has isolated you diplomatically in an absolutist environment (speculation, but that is how I would imagine it). Also you could support a rival's revolution to weaken them, and even if the revolution fails (maybe you don't want it to succeed in the first place), it can make a difference, because a bigger chunk of their country will rise up because of you.
-I don't think it will completely be up to RNG. If an AI (or your) country is mismanaged somehow and unrest is big enough, the revolution could be too big to stop (like the French Revolution), but in countries that are stable enough or manage to handle the revolution well, maybe the revolution will fail (or stop after some concessions).
I imagine the age of revolutions as a tug of war, not a switch flipping competition (maybe I didn't phrase myself well if it came out that way), and it could bring some spice to the endgame. I imagine it could put the empires (smaller nations too ofc) existing by the endgame to the test and if you managed your country well it could be a situation that you can manage well too.
Except it wasnt. The Ottomans lost and regarined territory all the time like every other nation. They didnt stop modernizing, nor was their modernization period far off other countries in the region. Not even the amount of rebellions were atypical for a multi-ethnical nation like the Ottomans. It is just that the 1870th in particular were very harsh on the Ottomans (first stock market crash, bankrupting the Ottomans, followed by a famine on the Balkans 1-2 years later, followed by a war-declaration by Russia 1-2 years later). That doesnt mean their decline was a long process. Post 1870th is just a ganking of European superpowers on the Ottomans, which would have turned out similar with any other Empire (take the Polish as an example).
My knowledge can lacking in the subject (very well could be, I never did a deep dive in the subject) but I always learned that after the second siege of Vienna they had a slow but steady stagnation/decline/lagging behind the rest of the continent (maybe with pauses and countermeasures here and there) until the dissolution of the empire. Of course it was still a huge empire (although that made it hard to hold together) which had might in it's own right. But if I was wrong here, maybe the Khmer or Mughal empires are better examples for decline periods.