Air in the heating system can be, at best, annoying, as it is often accompanied by blubbering and splashing noises in the radiators and pipes.
It can also prevent radiators from heating up properly as they no longer fill completely with water. As a result, it will take much longer than usual to heat up a room, using more energy in the process.
Air can also cause the pressure to drop, so much so that your boiler may be unable to operate safely, at which point it will go into a failsafe mode until the pressure is restored.
Bleeding the radiators is therefore not just about eliminating annoying noises, but ensuring the efficient and reliable operation of your heating system.