Why would someone solder wires between the USB-C port and the USB 3 pins?

That's a power injection mod, not a workaround for a broken connector. Those wires are feeding 5V straight to the VBUS pins on the USB-A stack, wich does one of two things depending on where the other end goes. If it just ties the USB-C 5V rail to the USB-A 5V rail, it's a voltage sag fix. The traces on the board are skinny and any decent current draw on the ports drops voltage before it gets there, so people solder a wire across to give the 5V a bigger path. If the other end runs off to some external supply point, it's backfeed, meaning the kiosk coud power the whole Pi by feeding 5V in through a USB device instead of the USB-C plug. Kiosk builders did both, sometimes on the same board. First thing I'd do is trace where those wires actually land. If both ends are just on the board, bridging the two 5V rails, it's the sag fix. That's harmless to leave in place as long as you only ever power it from the one source. The trap is powering USB-C from one supply while somthing else is feeding the ports, because now two sources are fighting each other and that can get ugly. As for whether to pull them off: if you're planning to run these Pis as normal single-board computers with a keyboard or a flash drive plugged in, the stock traces are completely fine and the wires are doing nothing useful. I've pulled similar mods off boards before and it takes five minutes with some solder wick. Just work with the board unplugged and give it a good look afterward to make sure you didn't lift a pad. But honestly, if they're clean solder joints and you can see where they go, leaving them costs you nothing. I'd only bother removing them if you want the boards back to stock for resale or you're worried about somebody later plugging in a powered hub and creating the two-supply situation. Functionally they'll run identical either way.

Yeah I've seen these on a few kiosk boards I picked up secondhand. Funny thing is, one of mine had the wires snipped in the middle instead of removed, like someone halfway undid the mod and gave up. Still had to clean up the stubs with wick anyway. If you do pull yours, take a photo of where they land first, saved me a head scratch on one board when I couldn't remember wich pad a fragment was coming off of.

Ran into one of these on a board from an old menu display unit. What saved me was a cheap flux pen, dabbed it on the joints and the wires lifted off with barely any heat. Before that I was cooking the pads trying to drag them free dry. I also traced the runs first with the continuity beeper on my multimeter, took two minutes and told me exactly wich pads each end was sitting on. Mine turned out to be the rail-to-rail bridge, so I left it in and the board has been fine for a year of light duty.

I strip these out of retired lottery terminals at my job, probly a dozen boards a month come thru with the same jumper. One thing nobody's flagged yet: look at the USB-A ports themselves for heat discoloration before you decide anything. If the plastic around them is browned or the solder on the port legs looks dull and reflowed, the previous setup was pulling hard current and the connector contacts may be worn. Swapped a port on one of ours last spring for exactly that reason, the wire mod was fine but the socket itself was toast. Also worth a sniff near the power section, burnt flux smell sticks around long after the fault.

Reminds me of the days we did the same trick on the early Model B boards, except back then it was soldering onto the polyfuse legs beacuse a couple of hard drives would brown the thing out. If you keep the wire, do yourself a favour and check it under load, not just sitting idle. Plug in a stick or two, put your meter probe on the 5V rail and watch what it does while the board is busy. Numbers tell you more than eyeballing joints ever will. I've kept a few of these jumpers in place for years without a hiccup, but I always test before I trust them.