I really think it depends on your goals, objectives, etc. and with what civ you play...if you're playing to score points, you want to increase happiness as soon as possible and obviously grab territory, all components of a high score. Therefore, moving up to at least Republic is necessary to achieve maximum happiness (as compared with Monarch or Depo...) and productivity, not to mention increased wealth (provided you don't have a huge military unit base).
Based on my own experience with China, in which I'm frequently at war, I like the flexibility that the Republic offers in the way of maximizing happiness and thereby increasing production, wealth, etc., all needed to support my massive military-industry complex that I try to build into the Modern Age...
The trick is, and I think this goes to the heart of the question, is how to go to war in a republic or democracy. There's a specific article that talks about this in the War Academy I'm pretty sure. But I've waged very successful wars (long ones too) at the Regent level based on these simple concepts:
1) TIMING...once my industrial complex is at full-steam...helped to a great extent by an early switch to Republic...I'm able to go into a War readiness mode. I don't think of starting anything militarily until I've reached this point. Sure I could do it in Monarch, but it takes much longer and if I'm playing for points, the earlier I can gain a happy pop and maintain it, the better.
2) LUXURIES...If you have a strong base of luxuries, you can use that later on in Republic or Democracy to ease the war weariness that is sure to come when war is declared. After I've started or found myself defending in a war, if I have the cash (generated through the help of the Republic) I can ease back on research (20-40%) and turn up the luxuries (20-50%) I can easily retain a positive cash flow while fighting a war and having a contented population
3) CASH...You have to make hay early in the game, building up your cash reserves (Wall St. ASAP, trading for GPT, etc. ) so that you can 1) support a large military 2) trade luxuries for tax dollars when you need to keep your pop happy during war.
I find that for myself (a moderate warmonger) Republic strikes a good balance between getting the increased production from Monarch and the increased war weariness of a Democracy.If you're not inclined to use your military to this extent, or if you're not going for points, I think you can get away with avoiding Republic or Democracy. But always be mindful of your opponents, especially the aggressive ones who WILL use their military and always do so from Republic or Democracy!