I remain baffled that alerts in modern browsers are still handled with an OS-level modal dialog that prevents interaction with the browser's interface elements.

Couldn't the alert instead be rendered as an overlay to the page itself, be modal to just that tab, and not disable the browser Chrome? This would make it much harder for pages to "trap" users with alert spam. The existing policies (don't allow this page to create more dialogs -> page instantly redirects to itself to reset the flag) aren't doing a good enough job.