This seems like a misuse of favicons. Is there spec for changing the icon that way? Are the icons you expect to change being served with headers that allow caching? Are there more appropriate APIs that could be used like notification API?
Think the the unread count for GMail or the new message notification badge for Slack. It's worked this way in Firefox and Chrome for almost 2 decades. We're past the "you're doing it wrong" timeframe, in my opinion.