This is just one of many reasons why a trainer tire should be used... A normal road tire is designed to be supple and provide good grip and wear charateristics on a rough surface, where you have minimal amount of heat generation. On a trainer, you have a fairly large contact surface on a smooth surface, which will generate heat (which is the lead cause to tire breakdown on a trainer) and as an added bonus, will provide sufficient grip on the smooth surface resulting in much less noise.

... and a trainer tire is not very expensive...