I believe the most important objective in construction and remodeling is achieving satisfaction for the person paying for it and/or living with it. Any stairs in my home will have a skid resistant tread,esp the front edge. My experience with stairs and steps in commericial inviroments where results are seen quicker than residential,is the front edge realy takes a beating. To see this happen,watch from the side of heavly traveled steps or stairs. You will note that 75% of people make initial contact on front edge with the instep of thier shoe. I love the look of all wood stairs with painted accents but taking all into consideration,I opt for carpet on center of treads including nose with wood on each end of tread and intire riser.

The reason not to do it is the wear factor, for the reasons klem1 stated.

However, just because that occurs in commercial/apartments/etc. does not mean it will occur that rapidly in your house.

Other factors include what type of wood is used, the type of use(daily one or two times versus 10 or more), the finish used, and the humidity/temp changes.

Pine stairs could be damaged on the first use. Ipe might never be damaged. Oak could chip off, while hard maple probably would not. Those differences are because of grain density and differences in grain structure.Pine and oak have a lot of difference, Ipe and maple do not.

Polyurethane finishes will be chipped and require recoating. The chipping would happen on bull nosed treads, but usually is less noticeable. Non poly varnish would wear, but not be as noticeable and repaired much more easily.

Less dense woods(oak/pine/etc) absorb moisture more readily than woods with more closed grain(Ipe/maple). That means more swelling in high humidity and more possibility of damage from chipping over time.