Is this how comping actually works? I’ve never worked in a restaurant, but I assumed there was some system for it (if sometimes ill-defined) and not just employees stealing.

The receipt printer in the kitchen is tied to the POS. Anything rung in for prep is saved in the computer. The manager can run reports and see who comped what and if anything has been voided. This has been a thing since the 90s.

Creating a good guest experience is how you get repeat business. Comps are part of that. You are talking about theft and I mentioned nothing of the sort. If you choose to engage in such behavior then that's your business - don't accuse me of it.