I once forgot my tennis shoes so I went and got a $15 pair of running shoes to play in that night. The rubber outsole that comes up to the front completely peeled off so I had a rubber flap hanging off the front of my shoe. I will never wear running shoes to play tennis again (well, so long as I don't forget my tennis shoes, that is)!
I am a big guy so I wear through shoes quicker than most but if you are not wearing through running shoes on hard courts at all then you are either a super-small person or you are not playing intense, fast-moving tennis, I expect. A higher level tennis (say, 3.5 or 4.0 and above) is going to cause wear on shoes due to all the quick stopping and starting, and such other things as dragging your feet on serves or volleys.