I live in a very heavy snow area in the North East US (Buffalo region) and we definitely don't "dig up every street every winter for repairs". What is usually done is that when the snow thaws and the temperature warms a crew will come out and fill necessary holes in the pavement, not dig up streets. This process is very fast, it only takes a few minutes per hole and would definitely not include digging up the streets.

Here in Germany we fill the holes every few weeks in winter, and then rebuild the street completely every few years when more than 50% of the street are those filled holes.