What Proton is doing to e-mail is about the same that WhatsApp, Messenger and others did to messaging - instead of just using an open protocol like XMPP they opted for their closed thing in order to lock people into their apps.
PGP is not closed. What proton has done is make a really cool JS library for PGP as part of their Web UI (openpgpjs.org) which other projects, even those unrelated to Proton have used, like Mailvelope. They're also pushing the PGP standard itself to support stuff like post-quantum encryption. So this is really odd to hear as Proton is, without a doubt, the most open and interoperable of all the properly encrypted providers.
Lavabit
With Lavabit, you were simply trusting them mostly blindly on their claims. Yeah it worked out that one time but could have gone very wrong.
Yes, they have it because GDPR does require it.
They've had it since far before GDPR took affect. They've also had bridge which has always allowed external backups and is in fact real time. They now also support forwarding mails, which should also suffice for your use case.
Open sourcing the server software is desired ofc, but would it really mean a lot for security? Not really. All the relevant bits are already open source. And none of it is really non-standard. But i do still wish for that for the sake of transparency. And yeah i wish they would move away from this almost source-available model.
Regarding SMTP, yeah i agree. But they do provide that through bridge and also for business users based on a per-request basis.
There are definitely a few artificial limitations and stuff that really pisses me off, like the limit on aliases in custom domains and SMTP for normal paid users, but a lot of the talk I'm hearing on lemmy about proton is just FUD.