Doesn't using the "system" webview throw out the main selling point of Electron, which is that you're shipping the browser, so you no longer need to support more than one of them?

Perhaps, but using the system webview also means that you don't have massive amounts of bloat, both in distribution and on-disk size as well as memory usage, and you have a better chance at getting better performance.

Besides, all of the relevant engines are WebKit variants, so you're not targeting Trident or Gecko or anything.

Bear in mind that a lot of popular "apps", like Slack, Discord, etc., are web apps anyway, so there's a decent chance that the "support more than one of them" problem is already solved anyway, meaning you don't have to spend any more development time but you get huge increases in performance and responsiveness.

That is very true, and it's a nice differentiator relative to Electron— you still get your own app launcher and access to system APIs, but without shipping and launching the entirety of Chromium.