I don't know. Maybe FTL travel was developed as a military technology for galactic-scale battles or something like that.
Again, this runs into the whole problem with how ridiculously far apart everything is astronomically. If you want to develop FTL for military purposes, this presupposes that you've already found an enemy to fight where FTL would be an advantage. Presumably, any non-FTL-capable race will be just like us: they won't have any idea if other intelligent beings even exist, so they wouldn't know where to go to find these new enemies. The only exception here is if two races developed independently on two different planets either in neighboring systems, or in the same system somehow, and learned about each other's existence somehow.
The fundamentals of modern physics were developed in the first half of the 20th century with two world wars.
The two world wars took up a large part of the first half of the century (and then the Cold War took up even more), but that doesn't mean that every advance during that time was created for the wars. Einstein didn't create the theories of Relativity just so he could build a bomb; theoretical scientists like that (who are much closer to mathematicians) aren't really thinking of practical applications early on. IIRC, he came up with a lot of his stuff while he was still a patent clerk.
Remember, the whole Industrial Revolution was still going on in the early 20th century. That drove lots of advances on its own, without any need for a war.
Even if I like your way of thinking, being a pacifist myself, I really believe it to be wishful thinking. Unfortunately.
Well, for what it's worth, I'm not a pacifist at all. But I only believe violence is necessary to secure peace, because so many people (e.g. violent criminals) easily resort to violence to get what they want at the expense of others. I think any highly advanced race will either simply not have problems with violence (sort of like ants, who only use violence against non-ants, and never against other ants of the same tribe), or will have figured out how to make themselves evolve (with genetic engineering if necessary) past the point where they're predisposed to it.
Finally, as far as galactic-scale battles go, why would anyone have them? Wars are usually over one of two things: resources or ideology (which includes religion). Advanced aliens are very unlikely to have resource wars; with all the uninhabited planets and moons and asteroids out there, and the fact that such aliens are advanced enough for FTL or any decent level of spaceflight, it should be pretty trivial for them to find all the resources they want in their own systems, or in the many uninhabited systems around. Why go engage in a destructive war with someone on a faraway planet if you can get the same thing without a fight somewhere else, probably no farther away? Secondly, advanced aliens are unlikely to be religious and want to convert all the other aliens they can find. They'll have evolved past the need for making up myths to explain the unknown and the afterlife. And finally, what kind of aliens are going to go look for other aliens (who might barely be recognizable as "life" to them) just so they can have a capitalism vs. communism war with them?