I’d be interested to hear a specific expansion on this point (“hide” how? etc). I think the gp raises some valid concerns.

Have your Gmail account pull emails from your in box, have Gmail send as if from your email address.

Exactly this - in "Exchange" terms they called it something like "smart host" if I remember. But basically you use a major provider to do the final "connect to the internet at large" but everything is on your machine and you could change your outbound routing at anytime.

Such an obvious solution when you point it out that way. Thank you!