IPv6's biggest problem remains not that it's badly designed (at least not nowadays, there were problems but they were solved ten years ago) but that millions of network engineers never bothered to look deeper into IPv6 than "I don't get it, this feels off". You can't make a backwards compatible "IPv4 with more bits" like people dream of. L2 routers and middleboxes would still need to be replaced, software would still…
I'm also working on a project to reclaim some IPv4 address space, which people often object to on the grounds that people should "just use IPv6". So I have to defend the legitimacy of the demand for IPv4 address space.
In connection with this issue, I recently ran some DNS lookups against lists of top 1,000,000 domains (the last Alexa one and the Cisco Umbrella one). What we see is that only dozens to hundreds of "top million sites" (depending on one's definition of "sites" and so on) are IPv6-only. That is, less than 0.1% of Internet sites currently have an AAAA record without a corresponding A record, notwithstanding things like Mythic Beasts's offering to sell this configuration to them.
The over 99.9% of sites that still have an A record have it for a very good reason, which is that somewhere around half of all of their users (of course, quite a bit more in some regions and markets, and quite a bit less in others) would be unable to reach them at all otherwise. This is probably going to be true for a long time, even if that fraction keeps creeping steadily downward, and there's not much the site operators can do about that.
On the other hand, maybe you're talking about things like the "A record but no AAAA record" case (sites that don't offer IPv6 support). This is around 45% of FQDNs that have any form of address record, according to my scans using recent Cisco Umbrella data. I don't particularly have a defense of this; in fact, I find it really unfortunate. I happen to also be involved with Let's Encrypt, and I've often seen a pattern where smaller site operators, at least, show no awareness of what IPv6 is and no desire to debug it (e.g. if their certificate request fails because their old AAAA record was broken). I think Happy Eyeballs has been kind of bad on this particular dynamic: small site operators will themselves perceive their sites as working fine with completely broken IPv6 configurations, and it can be hard to convince them otherwise!
I'd love to see some kind of tool, messaging, initiative, or whatever that would encourage the long tail of site operators to be willing to spend, like, three minutes learning that IPv6 is a thing and that it's good if they have it set up correctly rather than not having it set up correctly. I still don't know what that would look like. I've seen dozens, if not hundreds, of forum posts telling people various forms of "it looks like your AAAA record is out of date; maybe you should delete it".