So the affected hosts that need to be in this list is every shared hosting IP -- not just those that use LE, but all of them. They can then remove IPs once they verify LE-specific workarounds have been applied.
But they need to scan IPv6 as well.. since, although SNI is less necessary with IPv6, it can still be used with IPv6. So they need to scan the entire IPv4 and IPv6 address space (regularly.. to keep the list updated) looking for shared IPs. And we'll assume their scanner won't be blocked or interfered with in any way, so they'll actually be able to determine which IPs are being shared.
As far as a solution, I think I've been very clear in my other posts. The underlying assumption in this protocols is incorrect, and that makes them fatally flawed. They should be discontinued entirely (at least until we've all moved to IPv6 and SNI has been removed from the TLS standard).
For example.. if a number of domains are at a CDN (that does not use anycast)... they may all resolve to a single IP (to LE, from the location they're requesting from)... but really that CDN may have hundreds of IPs that are all valid for those domains. LE would then add that single IP to the list as a shared IP, but LE verification requests sent to those other IPs would still be vulnerable.
Even then, you have a CA sticking out its neck on the assurances of a web host that isn't accountable to the root programs and isn't accountable to the CAB Forum.
If that web host swears they don't have the issue, LE tests them, whitelists them, and then subsequently... at a customer request or just to be nasty the web hosts reverts and allows this exploit, the web host won't be held accountable. The CA will.
By the same token, if that web host were hacked and used to obtain a nefarious certificate, would the CA be accountable? It seems to me that, as a customer, if you point your domain (which you must do somehow) at a hosting provider, then any DV issued with that hosting providers' infrastructure should be considered to be the responsibility of the hosting provider and domain owner. I think you and rgbrenner are making perfectly valid points for high-value infrastructure, which has in my view very little to do with these hosting providers. The fact that people can upload certificates at all for domains which they have not proved (to the hosting provider) ownership of is disturbing in and of itself, even if it is quite common.
Even if... You would only know for the set of web hosts for the time period you checked each one.
New ones come and old ones die every day.
I think you underestimate the capabilities of modern infosec tooling. Essentially the whole of the internet can be scanned in some ways in durations measured in hours. What is more, some systems are being constantly updated (such a certificate transparency), and there are relatively easy ways to identify bad actors via whitelists and behavioral monitoring. All that being said, if you have a legitimately better idea, voice it in a meaningful way, and I am sure they will at least listen. That was the part _in_their_post_ about "taking community feedback" you must have missed.