If we would take the average number of supernovae per year and multiply that by the number of stars, could we figure out how many years it will be before all stars are gone?
Not that easy way. Only stars heavy enough will undergo a supernova explosion. The majority of stars is too light. The lifetime of a star is mostly determined by its mass. In some cases (supernova type Ia) a companion star provides mass to white dwarf, which originally has been too light to explode as a supernova.
Hence your technique can only work, if it is applied to stars of a certain mass and composition separately, and then summed or integrated up over all these restricted classes of stars. All together you'll get results for stars which eventually will end up as supernova, i.e. the heavy ones with more than about 8 solar masses.
... And in the meanwhile new stars will form.