I understand this is to “check our engine is still operating at idle”, but can someone explain this more in depth? Like why wouldn’t it?
Because, in engaging the carburetor heat, you are decreasing the density of the air entering the engine with the same fuel flow, thereby richening the mixture. At idle power, if the throttle idle set screw is not properly adjusted, there is a risk of an engine failure from too rich a mixture entering the engine. The idle power carb heat check is a good way to verify the engine won’t do this in flight.
Carlo Felicione has given a great explanation of why carb heat at idle would need to be checked. The incoming air heated by the exhaust manifold would be less dense than the incoming air without carb heat. If the fuel mixture is too rich, it may cause the engine to quit. Some may call it flooding the engine.
The most common time for this to be an issue is on final approach. In a Cessna 172, you set the mixture to rich (or best power) to prepare for a possible go around. You would set carb heat to hot in order to avoid carb ice during low power settings. This would be a bad time for engine failure. You are very low to the ground and at a very low airspeed. If the prop stops, you may not have enough airspeed over the prop to continue to windmill it for a restart. And, you may have very little time or mental bandwidth to kick over the starter.
While I have not had this happen on final in real life, I have seen videos of Cessna props stopping when the throttle was brought back to idle in flight. I have also had a 172N prop stop after landing at a field elevation of about 500 feet with carb heat on and mixture full forward. The same N model had no problems for the A&P check. But, the prop stopped later that same week during the run-up at about 500 feet of field elevation.
It performed perfectly during the higher run-up RPM carb heat check. It had a consistent drop in RPMs when carb heat was applied with a consistent return to RPMs when the carb heat was turned off. Idle setting was checked and functioned well at about 700 or so RPMs. The engine quit as soon as carb heat was applied at 700 RPMs. Obviously, that was the end of our flying day. And, I have never skipped the carb heat idle check after that.