On the basis that this isn't an entirely rhetorical question, two I know of are Kinsta and Pressable. We use Pagely, but I have some hand-rolled Bash scripts which perform the same function.

Thanks, it was intended as a bona fide question. Our company does use WP Engine, and while we could total insource it (we already manage our bread and butter app), to do so I'd have to recreate the staging (and ability to push to production) ability (already have some ideas on how to accomplish this easily), but I'd rather save the engineering cycles for our actual product.