I don’t think that’s true. But of course it depends how you’re measure the majority of websites.

Most of the figures I see show 60-70% of the top 100 sites do support it. But maybe that does not reflect your usage.

Why do you need it? Maybe you don’t right now since ipv6 only sites are niche. The most tangible advantage I’ve seen is avoiding CGNAT. Gamers in particular don’t like that because it introduces latency. Services like Xbox live definitely do support ipv6 for this reason.