The same idea exists in the US, and often bathrooms have a PIN code to enter or a special key only the shop owner has.
I’ve never been turned down when asking politely. Most people are rather sympathetic when someone needs to use the bathroom for legitimate purposes.
Business owners perceive the presence of homeless people as bad for business so they don't want to encourage homeless people to stick around. And they think homeless people will trash their bathrooms or use drugs inside which is dangerous for other customers and brings police presence.
So business owners lock up their bathrooms. Result: Even fewer places for homeless people to use the toilet.
These things aren’t just perceptions or thoughts. It’s a real problem that anyone who runs a business in a location with a homeless problem can attest to.
Businesses care about the first type because of the associated problems and are completely fine with the later.