I run it for my personal self-hosted infra, and it works really well. Setting a custom control server URL is relatively easy (at least on Windows and Android which I use).
I use taildrop, I serve docker containers to the tailnet, etc. headscale works really well and is worth a go.
The official clients (most valuable: the polished mobile apps easily installed from the default app stores) are one auto-update away from cutting ties when push comes to shove, the same as all commercial VPNs with a free tier.
However I do not think Tailscale is going to remove the custom control URL feature from their mobile clients. For one, I think there are legitimate "Tailscale Enterprise" use-cases for the custom login server.
Additionally, I have heard that Tailscale has been supportive of the Headscale project, providing assistance to the devs.
Further, Tailscale seems fairly committed to keeping their clients open sourced, and engaging in the developer community. Of course as you can say this can change at any time.
And of course the API used to manage the official server, so the rare things that depend on it won't work, but it's more a case that the project doesn't have the need to work on it