There's absolutely nothing stopping browser vendors from implementing ActivityPub. I don't think the browser is the right place, but browsers also implemented automatic RSS feed detection for more than a decade so it's not exactly unprecedented either.
Browsers don't need to care, anyway. There are some problems that need solving (notably, following/interacting with users on other platforms) but there are ways to do that. I'm not quite sure why nobody has come up with a good standard for a web-activitypub: URL handler, but once everyone agrees on a format adding support for cross-server stuff should be easy.
Web browsers can access webmail clients and mailing lists just fine. They even have mailto: as a means to cross the federation gap. All of these problems are implementation issues, not conceptual impossibilities.
Browsers don't need to care, anyway. There are some problems that need solving (notably, following/interacting with users on other platforms) but there are ways to do that. I'm not quite sure why nobody has come up with a good standard for a web-activitypub: URL handler, but once everyone agrees on a format adding support for cross-server stuff should be easy.
Web browsers can access webmail clients and mailing lists just fine. They even have mailto: as a means to cross the federation gap. All of these problems are implementation issues, not conceptual impossibilities.