Briefly regarding the republic tradition policy: The point of it, imo, is to allow you to keep your reelected leaders longer. It's not about how long it takes to pay back one re-election, since almost any modifier in that regard will fall on its face, but about longer stretches of re-elected 6/6/6s or the like. Since you can turn the policy on when you want, you can turn it on when your tradition is high anyway and your leader is young, then turn it off if you need the extra bird mana. Additionally, higher tradition decreases unrest
Regarding the idea group itself: It's one of my favorites though I agree that it's not the best. They have permanent manpower reduction, but they have permanent mercantilism increase as well. Also, the idea group events are drawn from a pool of all available events, which increases as you unlock new ideas, so the likelihood of this happening often enough to really impact your game decreases as the game goes on. My point here is not that it's not a shitty event to get, but that the impact of it is surmountable.
The idea group itself is pretty jack-of-all-trades and as a result most of the ideas worse than what you find in more specialised groups, but there are three shiny ones:
The -2 unrest is incredible and stacks monstrously with Humanity, easily resulting in having little to no unrest in newly conquered wrong-culture-and-religion-provinces.
The additional merchant is, I would argue, better for non-merchant republics who WILL take Trade anyway, as well as probably Expansion, and will be rolling in merchants. Rather, it benefits those not normally focused on trade since it allows a 50% increase in available merchants, allowing you to control your local trade for some extra bucks without having to run a country mile for that benefit.
Finally, manpower recovery, the last of the group's good ideas: Recovery is so good. It basically works as a 10% increase in manpower, yes, but it's also a buffer against Peasant's War, since you get back above 25% manpower faster, as well as overall allowing you to completely recover from a devastating war in 9 years instead of 10. 10% is less than you can get elsewhere, yes, but like unrest, it's all about stacking. Hansa with Quantity, Innovation and Plutocracy can go from 0 manpower to party time in 5,5 years, have reduced war exhaustion, extra leaders, plenty of mercs and money to fund the whole thing. They are the Duracell battery of human meat grinders.