Selfhosted Email... Kinda?

So I'm aware of all the challenges with selfhosting an email server, particularly with blacklists. That said, it would be nice to keep all of my emails within my own system. Out of curiosity, would there be a major downside to something like this:

• Email is forwarded to some inbox at some provider via a Cloudflare wildcard (I already do this to get everything into my Proton inbox)
• The contents of that inbox are pulled down to my own server via POP either at regular intervals or maybe via a webhook triggered on receipt of a new message
• I connect to my server via IMAP and can read my emails
• When I send an email, it gets sent via something like Brevo (which I already use for sending email notifications from my services)

In the end, what I'm actually selfhosting would just be the inbox, but that's all I really care about. Is this a sane setup or am I missing something here?

If this is a good idea, is there a particular provider y'all would recommend for the temporary inbox that my server pulls from? Could I feasibly selfhost the receiving server and just send emails via an external service?

Thanks in advance for any advice!