Flip it around for a second. You sign up for online banking. You use your GMail account as your e-mail address. You get banking statements in your e-mail, you can reset your password to the bank with that e-mail address, etc.
Now, a scammer is trying to access your e-mail account. What level of proof do you want them to have to offer Google to get ahold of that e-mail?
These tech companies are not asking for an "unreasonable view" into your life as long as people are using these products to interact with the real world. They are trying to strike a balance between convenience and security that meets real-world needs. And they are trying to set that balance point somewhere where it works reasonably for the majority of their non-technical users, not for the edge-cases and not for people who think LARPing as a 90's cyberpunk novel is the most important usecase. So, yes, so long as the vast majority of GMail users are using their GMail account in a number of ways that intersect with the real-world financial system, they are going to want some way to verify your real-world identity if you lose the log-in credentials to your account.
"you can reset your password to the bank with that e-mail address" - wait, what? That's not plausible at least where I live, since (a) this would be massively abused to drain people's banking accounts and (b) the bank would be fully on the hook for compensating these losses (above an initial 50 eur risk IIRC), so none of the banks would even consider permitting a risk like that, since that would cost them so much money.
If you need to reset your bank credentials (not solely a password - some form of second factor is universally required), it can't happen electronically without involving the real world; either you come to a branch with proper ID or you get mailed them to your registered physical address.
The standard solution for local online-only fintech services would involve piggybacking off of the existing secure electronic ID i.e. digitally signing the agreements (and the request for credential change) with the electronic signature key on your gov't ID chipcard.
I mean, no matter what you do, you have to have some root of trust / root of identity, and it needs to be backed by (and verified in) the physical world - so you either have to do it yourself or delegate it to someone whom you'd trust a lot (i.e. not a random email provider). If a trustworthy universal government ID is available (which is a problem in some places, like USA) then that is a natural solution to that.
Alternatively, an institution is free to trust people remotely, putting effort into fraud monitoring, and taking on whatever risk their trust and processes enable - e.g. we've had some financial institutions verifying passports over videochat in such cases; I have no strong opinion on how safe or risky that is, but presumably the institution has considered the risks very carefully and found them both acceptable and necessary (in that case, sending a scan/photo/picture of the same document was not allowed, it was specifically about live videochat) - which is the key part of the whole thing, the alignment of incentives and responsibility for that risk.
If the consequences of these security risks fall on the users, then the users have to worry about security while financial institutions just wiggle their ears and blame "identity theft". If the consequences fall on the institutions, then the users can stop worrying about the things they mostly can't influence, and the institutions magically design their processes and workflows carefully so that they actually prevent fraud (since it's their own money at stake) and they're forced to implement decent solutions to any tradeoff between usability and security, since their profits depend on both.
I certainly don't want my bank, dentist, phone company etc. to rely on a private, foreign company to decide if they trust who I am. Google are involved in stuff they shouldn't be involved in, access to an e-mail account should not be proof of identity.
Incidentally, in my country, there is a government-mandated (everyone has it) single sign-on solution that companies can use if they want to really know who someone is. The implementation isn't perfect and unfortunately they're starting to nudge people into using an app (that can only come from an app store, creating a sort of catch-22) instead of one-time pads, and there's a lot to complain about there. But I think the principle is completely reasonable, that just like we have passports, birth certificates etc., governments absolutely need to enter the digital era and provide modern forms of identity services. This is yet another area where everything moving to the internet has led to privatization through the back door, and I fear the world where some American company can turn me into a digital unperson much more than one in which my government can.
Now, a scammer is trying to access your e-mail account. What level of proof do you want them to have to offer Google to get ahold of that e-mail?
These tech companies are not asking for an "unreasonable view" into your life as long as people are using these products to interact with the real world. They are trying to strike a balance between convenience and security that meets real-world needs. And they are trying to set that balance point somewhere where it works reasonably for the majority of their non-technical users, not for the edge-cases and not for people who think LARPing as a 90's cyberpunk novel is the most important usecase. So, yes, so long as the vast majority of GMail users are using their GMail account in a number of ways that intersect with the real-world financial system, they are going to want some way to verify your real-world identity if you lose the log-in credentials to your account.