Don't do banking on your phone. The reason the bank signs you out is because of security

A ton of these requirements are due to regulatory requirements for securing access to accounts at the state and/or federal level.

Requirements are then interpreted by each financial institution and implemented by different teams. It's most likely due to the fact that a desktop is assumed to be more likely to be a shared device, while a phone/tablet is most likely to be a personal device, which is password/bio-metrics protected.

As for security around a browser: if you look at how phishing/hacking attacks happen on a desktop computer, if you can be tricked into launching an virus, it can copy all of your browser cookies and login sessions to the attacker, then they can duplicate your browser session. If you have an unlimited login for a financial institution, then they now have a logged in session for your bank.

https://www.reliaquest.com/blog/browser-credential-dumping/

So if you add up all that, then they're more likely to allow long term login sessions on an application that they control than on a desktop/web browser that they don't.

It is annoying, and they're definitely pushing people toward invasive smartphone apps using various means, but this particular annoyance has a good reason:

Browsers simply aren't as secure as individual apps, mainly because they execute code from other web sites as well. That means credentials available to a browser are only one remote exploit away from being compromised. And browsers are big, complex beasts with an unending stream of vulnerabilities waiting to be discovered and exploited. Tight countermeasures make sense for things as important as banks and medical info.

That's a safety thing. Phones are usually owned by one person or possibly shared in the family, but the security is such that app data is per-user anyway.

Websites though, people still sign in from all sorts of devices and often wildly insecure ones such as public/work computers, one malware away from hackers having access to your bank account.

Inconvenient for advanced users like us, but it would literally make all of those refund scams so much easier to pull off because they wouldn't even have to trick the victims into logging into their bank: blank the screen, transfer the money, tell them their computer is all fixed, bye.

My experience with my two banks has been, with their respective apps, I can sign in with just a password but I get logged out of the app after 10 minutes of inactivity. I never stay signed in. This is two different apps for 2 different banks.

On the web, they almost always request their crappy 2FA which is via text or email, and I do not stay signed in ever either, as well as being logged out after 10 minutes of activity.

What irks me is their 2FA, they have no other options besides email or text, the least secure options of all 2FA methods...

But being signed out everytime, I'm not sure I see it as that much of a hassle, and I kind of appreciate that if someone can unlock my computer or phone, they cannot open my bank account just because I was logged in 30 minutes ago...

I am failing to see any discrimination here.

The 4 banks I use all have the same policy. Auto sign out after inactivity from web. Web pages don't really know if a monitor is turned off due to inactivity so it is safer to log them out.
because who locks their screen when they aren't using their system?
When using an app, you have to re auth with a device specific pin or bio metric if the screen turns off due to inactivity or switching apps.

People tend to sign in and forget about it on computers, which are more often shared devices compared to mobile devices. That's one reason they might relax restrictions on mobile vs desktop.