The unworn 120 tire had a nice curved crown. When leaned over, the contact patch moves a bit off center relative to the wheel rim. This makes the rear of the bike "wiggle" when any side loads are present. The popular way to reduce this trait is to raise the tire pressure, essentially adding side loads to both walls and thus stiffen them. This reduces the crown's off center movement (for a while). However, increased pressures also raise the tire crown, making that part of the tire wear faster, and squaring off the nice rounded crown the tire originally had, and making replacement frequency more often.
Rubber actually fatigues with bending, making it less rigid. Important when considering sidewall stiffness. So, you either add more air pressure as the sidewall gets softer, live with the squirmy handling, or buy replacement tires. Of course, a new tire will feel better than the old worn tires, even if they are misfits. ... for just long enough to, implant fond memories, and generate repeat praises of the new tire brand via testimonials.
Putting oversize tires on narrow rims is great for tire salesmen. They get to sell you a more expensive tire at shorter intervals. Good for business. And bigger tires are an easy sell because all the newer bikes have that. Leading to the belief that putting bigger tires on their old bike's narrow rims is "upgrading".
A tire that is designed for the rim will perform better over the life of the tire, as well as extend the tire's useful life.
All the tire manufacturer's have a fitment chart, and most state the allowable rim width the tire was designed to fit. But beyond that, the bike manufacturer states what tires the bike was set up to perform as new. The confusing thing is that the tire manufacturer's have all changed their sizing criteria. New bike's have kept pace with current availability and supply parts that work with them. And in part, because tire marketeers and salesmen are pushing new tire "styles" as a fashion statement under the guise of promised performance, the demand for proper sized tires for older machines is low, leading manufacturer's to limit production of tires for the old bikes.
So, in part the reason for the limited choice in availability, is caused by buyers making choices based on faulty information. I don't think this will ever be "fixed".
