I've never seen one of those signs, but I drive a pickup and could suggest the issue is a sidewalk. Backing a truck into a spot can cause the bed of the truck to overhang whatever you've backed into, which could block a sidewalk or other walking path. Typically there is less overhang from the front of a vehicle to the front wheels than there is from the rear of the vehicle to the rear wheels, so pulling into a space forward wouldn't impede any walking path as much.

If the front of a parking space butts up against a residential area, people don't want their homes hit with exhaust particles every time someone starts their car.

I suspect that some paid places use automated license plate readers to check for non-payment, or could be checking manually but having all the cars front-in could still save the manual checker the labor of walking around cars.

edit: In recent years I've actually been in parking garages and seen seen a hapless security guard walking car to car, photographing the back of each one. (I've also seen 'meter-readers' doing the same thing in paid street parking areas.) I wouldn't be surprised if a car-mounted version also existed, which is what I meant when I speculated about automation.

I've seen this in underground or undercover parking spaces where there's a vent in the wall.

Is there a footpath there? Often tow hooks extend over the curb and can be a hazard and difficult for folks with mobility issues

Regaurdless, safe drivers always park so they drive out. you have much better visibility driving out than backing out which means you are less likely to run over something you didn't see. By backing in you had to drive past and thus had time to verify nothing was there.

Because all those guys who go on about how great reverse parking is are terrible at reverse parking.

Unless you mean parallel parking, because then it makes sense.

I’ve mostly seen them in parking garages so I assumed it’s for throughput.

• if you back into a spot, you’re holding up everyone behind you. If an impatient driver is too close you may back into them
• by fronting in, there’s essentially no wait, no risk of backing over that tailgater. When you want to back out, you wait until traffic is clear rather than block them

LPT: Not all signs are legally binding or even enforceable.

I've only ever seen those in parking lots where each lane is one way. They want you to pull in so when you back out you're heading the correct direction of traffic. But those also typically have angled spaces, like you mentioned.