Yes, absolutely.
All email providers will undoubtedly release all available information. Of course, a legitimate interest must exist, but authorities can easily obtain court rulings. If this is deemed sufficient, then companies like Google, Apple, Microsoft, Yahoo, Proton(!), and all the others will hand over everything they have, such as:
- Content of emails with attachments
- IP addresses
- Geographic locations
- Search terms
- Phone information (IMEI, etc.)
You can see what Google released in the Jeffrey Epstein case. Here it's a good thing, but I prefer to keep my email content private.
So.
You can rent a virtual server for a small fee and install everything on it. Those who don't want to delve too deeply into the technical details can use ready-made scripts or program suites like Mailcow.
I use everything individually under Debian.
Bind9, Exim4, Rspamd, ClamAV, Dovecot, Roundcube, and Sieve. Authentication is handled via LDAP.
The server is state-of-the-art, fully equipped. DNSSEC, DMARC, DANE, SPF, and DKIM, to name just a few features.
There's a secondary nameserver and a backup mail server, since lines and computers do occasionally fail.
A backup strategy with outsourcing to an external cloud is standard practice and has saved me several times.
The advantage is that everything is "in-house" and you're not dependent on external providers.
However, the configuration effort is somewhat higher.