> start putting up banners that say "our website does not work with your browser, please switch to Chrome"
That's how IE 6 was killed.
It was killed by a lawsuit, mostly.
Also FE devs using all new Chrome shinny APIs, and their Electron junk are also to blame, and they aren't going to throw their toys away.
The final death of IE6 was because corporates finally stopped using it⁰ and the reason for that had nothing to do with sites/apps refusing to work. If we'd said "we don't support IE6" they'd either say "the contract we signed years ago somehow says otherwise" or "fair enough, we'll use someone else's solution then".
What killed it was IE6 not supporting TLS1.0 out of the box or TLS1.1+ at all, and that started to make them fail external audits. After years of telling them IE6 was holding us back implementing best-practise security on their instances of our apps¹ and being ignored because doing anything about it their side was too much hassle, external auditors started refusing to give them relevant certificates & such because of their systems not being up to best practise (or even good practise by that point!) and suddenly they made the effort to no longer have anyone in their orgs using IE6.
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[0] source: I was working on software serving the banking industry (customer facing & investment sides, not trading) around that time and years either side
[1] Even having annual conversations like: