Thom makes it clear that a blocked static should be resolved by using alt static or breaking glass, therefore there should be no need to fly without those instruments which would be affected. However it is necessary to be able to recognise a blocked static exists in order to decide to use the alternative static sources.
Flying without an operational or accurate ASI may still be called for and Thom and 3 greens has the answer for that.
In the modern world a GPS will give you altitude but so should alt static.