I use standard 0.1" pin headers in my breadboards all the time. I haven't noticed any ill effects from using them. In fact, I find they work very optimally. The gold plated pin headers seem to slip in and out of the breadboard very smoothly compared to old and oxidized regular tinned ones.
The pins on those headers are square shaped with 25 mils on each side. Interestingly enough a 22AWG wire has a diameter of 25 mils. By this measure the pins should not put any more stress or tend to stretch out the springy contacts any worse than a standard 22AWG wire.
I primarily use the Radio Shack breadboards ("Experimenter 300"), and on the package they specifically recommend using 22AWG wires with their breadboards (although they advertise they are suitable for a wide variety of wire sizes).
In general the breadboards do get easier to use as they age, and the holes don't hold the wires in as well, but I have breadboards around here from decades ago (from my father) and they still work very well with 22AWG wires and standard component leads. Of course... YMMV.