Use a pre-compiler then. Gulp is so fast you won't even notice the compilation time.

Is there a secret I don't know about or do browsers convert LESS to CSS natively?

No, but there's a JS file that transforms your LESS into CSS in the browser. It's handy for development but obviously you'd want to pre-compile for production.

Is there any reason someone couldn't do the same thing for Sass?

The biggest issue is probably keeping up with Sass. Other Sass implementations are behind on features.

Less ... well, there's less to keep up with since there's one implementation of it that I'm aware of.

I used to prefer Sass, but mostly because it was the only thing going at the time, but I'm starting to lean toward Less.

looks plausible: http://medialize.github.io/sass.js/ :-)