Personally, I think that much of the wobble exhibited by Model 2 S&Ws may have occured by bending the gun. These are iron framed guns and the best guess is that iron or very low carbon iron/steel was used to manufacture in this era. This metal is quite soft/ductile and you can open the gap in the hinge by simply using your hands in bending the gun. Tucked into a back pocket or waist band and sitting on them is plenty of force to open the hinge gaps.
If you look closely at the hinge construction, you will find that the barrel has only one hinge sleeve and the frame has two hinge sleevess. Most of these well used guns will show slight space between the hinge sleeves and only a very small gap will allow the barrel to wobble. The screw is the pivot pin and the hole can wear with lots of use as well, but I have been able to bring back almost every loose Model 2 that I have owned by simply compressing the hinge sleeves on the frame. The hinge placed in a smooth face vice and compressed until the barrel fits tightly into the frame will totally eliminate any movement. Keep compressng the hinge and checking until the barrel takes force to install and that will take care of the issue. This option is only for unmolested non-modified guns.
I do not believe that shooting has much of anything to do with the wobble of the gun, but rather the lack of oil and excessive use can result in the pivot hole wearing, but 90% of the time it is the spreading of the hinge sleeves on the frame that is the culprit. I have played with and shot these guns for the last 40 years and have never cracked or broken a hinge, but am still nervous every time I perform this repair. I believe that the very first Model 2 I bought for under $100 back then is still shooting and as tight as new after this repair. Probably shot 1000 rounds of navy Arms 32 Long through it by now.
For me, this is a viable option to bring back to life guns that have been shelved for a long time and BTW, usually the cheapest to purchase out there as well. I have always looked for the loose ones.