Sometimes there is a sign saying "front in parking only" and I get it for angled parking spots but why would a sign like this ever exist for normal spots?

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.

Even without the sidewalk. Tons of trucks back in and take the front of the space behind them, basically turning them into compact only spaces.
For sure, it’s really annoying how far a pickup can intrude over the sidewalk. Especially with a tow hitch, and a tow hitch can be painful in the shins.

There a general problem in the US where we’re so car-centric that many don’t seem to expect people will ever walk, even on the sidewalk.

Or maybe it’s the recent loss of empathy

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 think this is it. I've only ever seen those signs in parking garages. Not all states require front plates, so I think they want to be able to easily see the back of everyone's car.

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

Yes, that makes sense. There are also light poles and things people might back into.

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

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.

Safe drivers are just that, no matter how they park. If your visibility is bad when you park front in, then either you're hauling something that's blocking your line of sight (in which case it would make sense), or your vehicle has terrible visibility, which is far too many of them.

Park how you want to park. I've never had a problem backing out of a space.
- If your visibility is bad when you park front in, then either you're hauling something that's blocking your line of sight (in which case it would make sense), or your vehicle has terrible visibility
  
  Or, you know, you have two vehicles parked on either side of you. Bonus points if they're two fullsize trucks/SUVs while you're in a sedan.

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.

That’s irrelevant. There was probably a reason for the sign. A conscientious driver will assume they had a valid reason and work with them, regardless whether it’s enforceable or likely to be enforced.

Do the right thing even if you may not be caught
- Oh I'm sure there was. Unlike my neighbor who put up an official looking "No street parking" sign in an attempt to keep people from parking in front of their house. It lasted maybe 2 weeks.
  
  Always question authority.

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 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.