Directly steered nose wheels of the Piper range are a problem because the nose wheel can be aligned sideways on touchdown but 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 to those used for training .
Sounds like a design flaw. The plane where I had the front tire go flat was a Piper Warrior II.
Perhaps a better designed cowling would help keep the nose wheel better oriented upon landing???
It was a club plane, but you had to be a fully certified pilot to join. No students, and most people flew the Cessnas. I learned to fly elsewhere on Tomahawks, then Warriors, so I was one of the few that used the Warrior on a regular basis.
I think I knew how to make decent landings by then…
P.S., I learned to fly in California, where planes bake in the sun at least nine or ten months out of twelve.