Don't blame the tools, blame the operator ;)
I ride nearly always in spurs, and never apply them unless I have to. I've given a couple of horses a few good thumps with the leg when they have barged into it - and have never caused spur wounds.
This is why you don't wear spurs unless you have a perfectly quiet, controlled lower leg in all paces, and if the horse is giving you some trouble. Until the leg can be 100% controlled, don't add a spur to it.
When the leg CAN be controlled, adding a spur is a brilliant way to improve the sensitivity to an aid - particularly in the lateral and collected work.
However, I don't understand why your instructor says that spurs will replace the use of the bit?
The spur is a driving (forward) aid, while the bit is a restraining aid. If you are over using the bit, you shouldn't be adding spurs, but working on your seat so that you do not rely on the reins.