We need to regularize in order to declare with confidence that infinities drop out from measurable quantities, e.g. in the form of a cutoff scale. In general, the amplitudes in QFT depend on the regulator, e.g., the cutoff scale $\Lambda$: $$ \Gamma = \Gamma(\mu, \Lambda)$$ where $\mu$ is the scale at which we evaluate the amplitude.
However, the difference between a given amplitude at two different energy scales is actually independent of $\Lambda$: $$ \Gamma(\mu, \Lambda) - \Gamma(\mu', \Lambda) \propto \ln(\mu/\mu')\, .$$ In this sense, the regulator drops out from measurable quantities and with it the dangerous UV infinites.
Therefore, I was wondering if renormalization is really mandatory or just a convenient method to make calculations simple?