There are actually two different failure points (at least) on Cessna main landing gears.
Many of these (most?) are the result of the gearbox in the fuselage failing, as a result of extreme forces applied to the main landing gear LEGS. Others are failures of the gear leg itself, in the area of the axle attachment, typically cracks originating at the axle bolt holes.
In general, both these types of failures tend to occur more frequently in tailwheel aircraft.....a ground loop being the most common starting point for gearbox failure and lots of off airport, large tires, and especially ski ops being more common for failure at the axle attach point.
Both these types of activities are much more common in tailwheel types, not to suggest that tri gear aircraft aren’t used off airport or on skis, it’s just much less common.
And, of course, while it is possible to ground loop a 182 (focus and determination are, after all, formidable skill sets) such events are rare. While ground loops are relatively common in tailwheel aircraft.
That leaves us with damage to gearboxes that’s discovered during routine maintenance. And, again, I suspect the primary denominator between aircraft will mostly be determined by the type of use and terrain that gear has been subjected to.
A thorough inspection of gearboxes is a good idea, but it can be hard to see some damage without removing the gear. I know one operator in Alaska (a Part 135 operator) who had his landing gears dye penetrant tested periodically due to operation on wheel skis. A bit extreme, but this was a “power user” operating in tough conditions. And, he’d had a failure of a gear leg at the axle attach.
MTV