I, too run off the edge in many situations. No big deal. The bench is plywood - nearly impossible to damage the wheel.
Brush off the bench frequently, often and lots!
I dip - sometimes.
I easily get a decent year from a basic $10 Fletcher with a small, carbide wheel.
My cutter compulsions / recommendations are maintenance habits: I constantly make sure the wheel turns easily and I store the cutter in its box or a jar with oily cloth in the bottom. Protect the wheel!!! If it gets nicked or the axel becomes loose and the wheel wobbles, you won't get the cut you expect.
Don't hesitate to test the cutter on some scrap clear glass. Look at the scratch. Are there skips? Does the line get a bit wide in places? Time to replace the cutter.