I can't speak for Foundation, but I do know that - especially with outgoing emails - self-hosting these days is a pretty big challenge.
Some providers will immediately flag your emails or delete them outright due to too strict firewall settings. Imagine a customer not receiving a response because their email provider didn't let Foundation team's reply through. That will probably be the main issue.
Sure it can happen, but every serious company in the world have their own email with domains, it would be silly if everyone would use just gmail.
Blocking usually happens if people are using shared hosting, and I am not 100% sure but I think that ledger and trezor considered switching to self-hosted emails after leaking of their newsletter with third party partners.
Oh, it's not about using a Gmail domain; Foundation Devices do have their own domain and use it for support emails. It just appears on the backend they use Google.
And that's what the vast majority of companies does (if it's not Google, it's a different third party email provider), no matter what the domain is, which you see as an end customer.
As far as I know, truly self-hosting your IMAP and SMTP and getting all emails to come through is one of the hardest things on the internet..

But I'd be happy to be proven wrong e.g. through a written guide on how to set up self-hosted email with high success rate!