Spinning itself actually puts very little stress on an airplane. It's the pull out from the dive that puts on the most stress, and unless that's done really ham-handedly, that's not all that bad. As for gyros being adversely affected, the DE I had for my commercial, IR, and CFII had a C152 Aerobat that he used as an aerobatic trainer and as an instrument trainer. When I was doing my CFII oral with him, we were chatting over lunch, and I asked him about having the same airplane for aerobatic and instrument training. He poo-pooed the idea of damage to the instruments by telling me that his airplane had about 1600 hours on it at the time and the original gyros worked just fine.
Mike makes a good point about what mods can do to spin authorization. For instance, any airplane which was authorized for spins that has an Avcon conversion loses its authorization, because the folks in Kansas didn't go through the necessary STC testing process. Since there is a weight penalty of about 35 lbs. going from the Continental 300 series to the Lycoming 360 series in the conversion which also affects balance, it's enough of a W&B change that proper flight testing would have been required to maintain the spin authorization. There's less of a weight difference between a Lycoming 320 and a 360, but the same rule applies--spins aren't authorized.
As for spinning 172s, they actually will spin pretty well, but they're hard to start spinning, and full spin inputs must be maintained to keep them there. They spin more easily to the left than to the right, although once in the spin, they spin about the same either direction. I always found that starting with a little power, like about 1500 rpm, was necessary to make a good break. Leave the power in for the first half turn, then pull it off, and recover when you decide to, using normal PARE recovery (power off, ailerons neutral, opposite rudder until the turning stops, then elevators to neutral to unstall the wing, then pull out of the dive). On 172s, it's not necessary to shove the yoke forward hard--the word "smartly" comes to mind (that's not true of all airplanes--with some, full forward yoke/stick is necessary). The 172 will stop spinning after roughly another half turn, sometimes a little less, after opposite rudder is applied (again not true of all airplanes--some, especially after several turns, can require as much as another 1 1/2 turns after opposite rudder is applied).
The only critical item about spinning 172s specifically is that they must be within the utility W&B envelope for safety--for all practical purposes, that means 2 in front, no weight in back either in the seats or baggage area. A CG that is too far back will likely make the spin flatten and much harder to recover, if at all. A critical item about spinning most airplanes including the 172 is maintaining neutral ailerons--failure to do that can aggravate the spin.
In olden times, CFIs were required to be quite proficient in spins and spin recovery and demonstrate that proficiency during the checkride. The Inspector I flew with required recovery within 10 degrees of the direction he specified. Now the requirement has been relaxed, so that the reg says the applicant must:
(1) Receive a logbook endorsement from an authorized instructor indicating that the applicant is competent and possesses instructional proficiency in stall awareness, spin entry, spins, and spin recovery procedures after providing the applicant with flight training in those training areas in an airplane or glider, as appropriate, that is certificated for spins; and
(2) Demonstrate instructional proficiency in stall awareness, spin entry, spins, and spin recovery procedures. However, upon presentation of the endorsement specified in paragraph (i)(1) of this section an examiner may accept that endorsement as satisfactory evidence of instructional proficiency in stall awareness, spin entry, spins, and spin recovery procedures for the practical test.... [unless it's a retest because of deficiency in that proficiency].
In other words, now a CFI applicant can show up in an airplane not certificated for spins, and so long as he/she has the endorsement and can adequately describe spins and spin recovery, that's good enough. In my view, that's not good enough, as it's too easy for a student to put an airplane into an incipient spin that requires prompt instructor intervention. I think any instructor must be truly proficient in spin recovery.
Cary