We did a similar thing, but folded it into unsupported and deprecated - unsupported browsers will get an HTML page extolling the virtues of updating your browser once a decade, whilst deprecated browsers (basically IE10 at the time tbh) were treated to a popup explaining that whilst the site probably works just fine, their browser wasnt fully upto date and the experience might suffer.

Eventually, and I doubt we had anything to do with it, IE10 usage dipped below the magic .5% (when it costs is more money to support than it earns us) and it was finally unsupported.

The only crappy browsers we still officially support are ancient safari and IE11, both of which are still going relatively strong for reasons we've never been able to fully explain!