No. Those issues will more likely be caused by smashing the wheels into a curb or stairs going up them and not using your weight over the bike to help the wheels up. A hard impact like that can cause a pinch flat if you are running tubes of possibly damage the rims too depending on the severity of the hit.

Tyre pressures really do depend on what type of riding you will be doing and your terrain.

50-55 is good for trying to stop pinch flats if you are running tubes and for running around on pavements and the like keeping your speed up by trying to have less deformation in the tyre to make your rolling resistance marginally less.

Conversely if you are riding off road then you want less pressure as that helps the tyre deform more, increasing the amount of tyre that is in contact with the ground at once and there by increasing your grip levels.

Damage like that is more dependant on the way you ride your bike and tackle obstacles as no amount of pressure is going to protect your rims in your just plough through objects. If I'm riding on tarmac with my MTB then I'll usually add a bit more pressure but only up to about 30psi (this is tubeless though bear in mind) and stair sets are not an issue.