There’s no technical problem with the idea; but I would worry that smoothing over the problems some pages have when rendered with anything other than the Chromium renderer, would just cement Chrome’s hegemony, since nobody would have any incentive to fix Chromium-renderer-only pages any more.

Perhaps it would still make sense specifically for enterprise use-cases: if the whitelisting (blacklisting?) of sites to trigger the compatibility mode on was only ever manual, or due to GPOs/MDM profiles, but never by predefined compatibility lists or extensions or auto-detected, then it would only get used in practice by enterprises who needed it for their legacy Intranet sites. Corporate Intranets are certainly where most IE-only websites reside these days—but is the same true of Chromium-renderer-only websites?