Some of the rules "cast in stone" are carryovers from the time when flying was mainly in taildraggers. Into wind is *always* a good idea in taildraggers.
With tricycle gear, there is less trouble of course with cross/tailwinds, but rather then have to concentrate on holding or stabilising bucking controls when doing run ups, into wind is sensible in stronger and gusting winds.
Of course the other oldie is "never taxi faster than a brisk walking pace", I understand mainly derived from the days when a wingman physically walked beside the aircraft and stabilised the wing of the early light taildraggers in gusty conditions. If we all taxied at a walking speed of about 5 km/hr it would take 12 minutes to taxi 1000m, at 10 km/hr about 6 minutes - fun backtracking delays on a lot of runways!!!! It's probably still trotted out to slow down newbies from taxying faster than they can coordinate the pedals.....