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.