I used to make a lot of kit beers. I got tired of hops, plus I'm interested in history, so I made a few batches of unhopped brew, in an effort to see what it might have been like before hops. It was a bit like home brewed cider: crisp, tangy, and refreshing. It lasted just as long as beer, and it had all of the characteristics of beer, save for the bitterness and smell of hops. I've read that hops was just one of many nasty herbs that people threw in their brew, in attempts to keep the flies down, which is the only (dubious) preservative effect. (I never kept any brew long enough to need to preserve it.)
And stability? Well, my brews didn't change in any bad way, so only the imbibers lost stability. So I think the pseudo-scientific claims of the benefits of hops suffer under scrutiny. They did under mine.
The reason we put hops in is because we put hops in, and we haven't done it any differently for hundreds of years. Of course we've developed a taste for them: there are no options. If you don't like hops, don't add them. It'll be fine. (But it won't be beer.)