The turn co-ordinator is a useful backup in case the vacuum pump fails, and the vacuum / gyro driven instruments (i.e. the DI and AI) all stop working. Combined with the VSI, and the compass, you can cross reference them to confirm you are straight and level.
The turn co-ordinator also indicates the angle of bank for a rate 1 turn (although if you know its e.g. 17 degrees in your plane), then you can also use the AI to do a rate 1 turn as well. I think partial panel training is still part of the PPL (it certainly is for the IMC training), so it gets used there quite a bit too.