In a recent game, my neighbor England declared on me early and I ended up taking her capital. She had one other city and I left it alone. However, because it was a decent city in terms of tiles and pop, she was still able to build wonders and even worse, because of her UA (extra spy), she was constantly throwing coups against my CS allies. All game I regretted leaving her alive, particularly since it was pangaea and I went for a domination victory (eventually ticking off the other civs regardless).
In vanilla it was worth keeping civs alive just so you could sign RA's with them at some later time (even if you had to fund both ends of the deal). But since you need a DoF now to sign RA's, and you will never get a DoF with a civ in which you took their capital, it's not worth keeping them alive in most cases as they just end up being a pain in the butt in the long run.