One benefit is to obtain SSL certificates using Let’s Encrypt or similar, which is nice to have even if you’re only hosting services on a LAN/VPN, to avoid certificate warnings (and to benefit from using a reverse proxy). You can use self-signed certificates, but this is annoying in its own right.
You technically don’t need to buy a domain for this since you can use a free DNS provider, but you can use shorter names and sometimes there are cases where you might need to switch DNS providers, in which case you have to change that domain everywhere, which is quite disruptive. If you own your domain, you take it with you when switching DNS providers.
One benefit is to obtain SSL certificates using Let’s Encrypt or similar, which is nice to have even if you’re only hosting services on a LAN/VPN, to avoid certificate warnings (and to benefit from using a reverse proxy). You can use self-signed certificates, but this is annoying in its own right.
You technically don’t need to buy a domain for this since you can use a free DNS provider, but you can use shorter names and sometimes there are cases where you might need to switch DNS providers, in which case you have to change that domain everywhere, which is quite disruptive. If you own your domain, you take it with you when switching DNS providers.