This of course is nonsense. It takes some effort to host your own, but you can do it, and there are hundreds of email providers out there. And there is the middle ground of getting your own domain and “hosting” your own for $6/month with Microsoft 365 for example…
I recall reading here a guy complaining that self hosted emails we're super prone to blocking because they didn't come from a reputable Domain/address, and weren't whitelisted from some of the big guys
Which is kind of the problem, if you need to be approved by the Big guys, there's not much of a point of calling open and fair
You still can host for sure, but the moment M$/Gmail, blocks you, you've lost contact with half the people
IP and ASN reputation really matters, as does having SPF, DMARC, DKIM and Email Feedback Loop (FBL) properly configured.
That being said, there are production mail servers on OVH (bad reputation mail wise) that deliver plenty of mail to Microsoft, Google and Apple mail servers every day.