It's not that adversaries can directly see the domain name; this doesn't have anything to do with domain fronting. The issue is that ECH doesn't hide the server's IP address, so it's mostly useless for privacy if that IP address uniquely identifies that server. The situation where it helps is if the server shares that IP address with lots of other people, i.e., if it's behind a big cloud CDN that supports ECH (AFAIK that's currently just Cloudflare). But if that's the case, it doesn't matter whether Nginx or whatever other web server you run supports ECH, because your users' TLS negotiations aren't with that server, they're with Cloudflare.
I can't speak for anyone else but I think I can work around that by moving the site around to different VPS nodes from time to time. I get bored with my silly hobby sites all the time and nuke the VM's then fire them up later which gives them a new IP. I don't know what others might do if anything.
If I had a long running site I could do the same thing by having multiple font-end caching nodes using HAProxy or NGinx that come and go but I acknowledge others may not have the time to do that and most probably would not.