Not going to happen overnight and even then technically they cannot access your emails because only you hold the password to private keys (if you trust they encrypt your emails with your public key before storing). I prefer keeping my emails local so pop does the job.
Google can access your emails but something like protonmail can't (if you trust them to encrypt your emails).
Sounds good... in theory. Truth is we don't know this, their mail client is proprietary and even if it was open source we still wouldn't know what their servers are logging. I am in a similar situation and I trust Google more than ProtonMail with all that Tesonet data weirdness pointing back to one guy. These shell companies can go and disappear overnight, something to consider.
Trust is multiple things. I "trust" that Google will manage my private Gmail account consistent with my expectations—which are effectiveness and long-term durability. I have no expectation of algorithmic privacy and thus there's no trust to break there.
3rd option. Running your own for incoming, using a service for outgoing. You get all the trust benefits of running your own server without having to worry about IP blacklists or any other crap. The nicer ones even generate your SPF, DMARC entries you add to your DNS.
I like also that it is no problem to use in countries which block VPN, like China. I had no problems accessing Posteo, but no way of accessing Gmail.
It also does not nag me every single time I change the VPN server I use, because I seem to be in a different location. I know this is supposed to be a security feature of Gmail, but man is it annoying not to be able to access your mail, because of that.
In Posteo you can also activate 2FA afaik, if you like such thing.
It just works, and I am glad to be able to give support to free software, while at the same time I also gain from it, by having an e-mail service, which is ethically way more acceptable than Gmail and is working very well.
Curious about the thought process that made you arrive to this conclusion.