I don't think OP is talking about products which consist entirely of front-end code, but rather analytics or tracking services which rely on front-end JS to collect user data, which is then used by the main product.
For cases like MixPanel, I don't see why the traffic wouldn't be proxied through the original domain. Unless MixPanel needs to (i) ensure that the property is not faking their stats/events, or (ii) track visitors across sites, the fact that the JS etc. is served from MixPanel directly is more of a convenience than a necessity.
The same would not apply if MixPanel were providing a verification service to third parties, who were advertising on or wanting to buy MixPanel's customer's site.