If they weren't based on FOSS we would all be running Firefox and Opera now, not MSIE (Firefox was popular on desktop before Chrome existed, as was Opera on mobile). Or perhaps they'd have forked Firefox/Gecko instead, or collaborated the effort with these projects. Safari and Chrome are merely a wheel in the larger ecosystem of Apple and Google, a means to an end.
Aside: you could make the argument that both Chrome and Safari are only open source because they were not built from scratch.