Does the cutoff really have to go to infinity in QFT? It seems that once we replace bare parameters by experimental (i.e. physical) parameters, the cutoff vanishes from the expressions for physical quantities, so it didn't matter what the value of the cutoff was, whether it's 0, 10000000000, or infinity. So do you really have to take the step of setting the cutoff to infinity after replacing bare parameters with physical parameters? It doesn't do anything, right, since the final expression doesn't involve the cutoff at all, so the cutoff can be any value and that wouldn't change the value of physical quantities. Also, say the cutoff is 10000000000, and you conduct an experiment at the same energy (10000000000). Does the bare parameter then equal the experimental parameter?