Off the top of my head, Firefox is probably the only remaining major browser that can still use a pagehide or unload events to do anything that actually posts back data, or do anything more complicated than confirm navigation away. Chrome and every version of IE or Edge I support doesn't allow a post during those events (to prevent the JS from hijacking a zombie tab). When Firefox encounters that event, there is no issue at all with the data post. In my case, my code actually owns what's in that post, but the content could write basically whatever it wants into a pagehide event and, with Firefox, it'll probably go through if it's fast enough.
Another thing I just thought of is string templating in JS. IE in no way supports it, and some of my clients mandate browser usage around that. I don't use JS string templating because I must support IE back to IE9, but it stands as an example of how browser bans may not be security related. There's this narrow chance that an inbound piece of infrastructure might simply not be compatible in some way they haven't been inclined to mention.