I don't know how realistic the approach in general is but "This site only works in ${SpecificBrowser}" or "Your browser does not support ${'Standard'}" banner refusals have yet to result in a business getting sued for not displaying properly in an arbitrary browser that isn't supported.
I think the reason behind that is simple: In my experience, there are orders of magnitude more not-entirely-ADA-compliant websites than there are sites with banners such as the ones you mentioned.
But yeah, I don't know if the site-isn't-compliant-in-certain-browsers-equals-discrimination argument would succeed or not. But I bet the people whose income dries as a result of browser-based-compliance up would definitely try that tactic.
I disagree. If there are orders (orders with an 's', meaning more than one order) of magnitude more easy targets, why would any lawyer go after a rarer and harder target? That makes no logical/financial sense.