This problem exists because for a successful empire in these games, you need a variety of techs, most of which are the early game ones. It's not even a balance problem so much as it is a fundamental capacity problem. You can't be an effective warmonger without the production to back it up, and production is economy based. Research is economy based. Diplomacy is sure helped if you have a strong economy to back it up (and switch to troops to defend yourself if need be).
Everything else is based on the economy, so any early techs that are economic in nature are required. After that, branching can happen.
Fixing it is a lot harder then you might think. The best way to do is to set the "base" level you start with higher, make techs comparatively weaker in the early game, and make research a lot slower. At that point you've got no real choice but to specialize in something early on, because dabbling in everything just gets you a lot of weak techs and research is slow enough that it takes too long to catch up on stronger ones. Unfortunately, 25 turns between techs and 300 turns before you get a really powerful one doesn't pass the "fun" test very easily.
You could also accomplish it by divorcing research from the economy entirely, but that means the main goal of building up an economy is to build troops, so you'll get more warmongers (as a millitary is essentially free when there's nothing else to direct the economy to do anyway).
Elemental is subject to this problem too. Want to be a warmonger? Great! The warfare line has lots of good tech for that, and you can get to it early... but you need citizens to turn into soldiers, and resources to make armor. That means you need towns, and houses. That means you need to get a farm on that fertile land you started off at. Farming is of course in the Civics line.
Want to research the spell of making? Great! Shame you need several labs to get enough researches to do it before anybody else, and you are limited in the number per town, and town size, and you'll need an army to defend yourself when other people realize what you're doing and come to stop you... so you'll need to build that farm. Back to the Civics line for you.
You see where I'm going with this. Town count, size, population, and resources are the limiting factors on warfare, research, defence, and so on. All of those things are economic and improved in the Civics research line. If you're playing on a large map, rushing to do anything other then build an economy is going to end badly. (On a small map, you could theoretically rush build an early army and go kill someone before they can react.)