I’m told that the tire/tyre in the nose gear can rot out because the front tire gets such little impact relative to the mains
I wish that was true, aircraft tyres rarely last long enough to rot. Unfortunately the nose wheel takes a hammering at most flying clubs/schools and the nosewheel tyre changes and undercarriage repairs are the witness.
They just deflate for no good reason, then tube is ruined.
Most go flat just after turning off landing.
Poor cross-wind technique and sideways landing owing to parallax are both guilty as well as from landing too fast. Tyres are required to go from a zero speed to a speed that is equal to that of most vehicle highway cruise speeds but in an instant. Operators from grass airfields report much better life from tyres in comparison to tarmac operations. Unnecessary and over zealous braking on grass will bite you but on tarmac it can be the all too common technique, especially when in order to take the early turnoff.
Directly steered nose wheels of the Piper range are a problem because the nose wheel can be aligned sideways from rudder input during the touchdown even if for no aerodynamic reason. The Tomahawks is infamous owing to this problem. The nosewheel assembly is attached to the forward section of the engine frame and requires regular expensive repairs especially those used for training. The sideways position of the nosewheel isn't confined to the landing but also the take-off. The Tomahawk requires quite a high speed before the high tailplane is capable of lifting the nosewheel weight. During the long period whilst the necessary speed is gained the tyre will be scuffing throughout a crosswind take-off.