There is luck in the game, as in real life, so what's the problem?
The problem is that you have yet again failed to present a single thing luck accomplishes in a strategy game that can't otherwise be accomplished by better design, and in fact never even tried. The problem is that you insist on (selectively) using reality in your arguments to support an unrealistic game element in an unrealistic game. The problem is that you have now twice repeated the same canned junk that is used on literally every strategy forum everywhere when a poster can't come up with an actual justification for his position.
Regencies are very powerful from a diplo perspective, which can win you the game as a small nation.
This doesn't make sense.
Granted, if I'm playing OP Castille or England and can colonize, I'd rather get a regency than their trash rulers too (though constantly playing two of the game's strongest starting positions isn't exactly the best thing for varied/strategically deep gameplay). While you *can* get into wars as a regency, you can *not* consistently take over as war leader or pick your targets. Your flexibility is massively gimped, and the attempt to use "realism" there falls flat; regencies did declare war in history.
The best argument for them is the "make monarchies weaker" argument, but with the changes to PU mechanics I would rather have a republic outright, expressly because you're guaranteed against utter junk and having progression slowed down/blocked...not to mention the hidden benefit of using low RT to farm mercantilism.