Left turning tendency is a function of pilot throttle control. If you rapidly open the throttle then even with a light crosswind the initial response would be a left veer. Once RPM stabilizes then the effect of a 90 degree 5 knot x-wind would begin to turn the aircraft back to the right. Depending on flap setting, the aligning effect of the landing gear could easily be overcome at low speed.
Have I ever needed to apply left rudder in a 172 in a light x-wind?
Yes. During a soft field departure full power is applied rapidly and the nose wheel raised as soon as possible. The increased angle of attack reduces the weight on the gear quickly and the slow speed with no nose wheel steering make the rudder very ineffective, therefore not just some left rudder, lots.
In normal takeoff from a paved runway, there is no excuse for the aircraft to not track the centerline even at relatively high x-wind components. 0 flaps, ailerons into the wind, proper use of rudder during smooth application of power, do NOT take weight off the wheels until the aircraft is ready to fly, rotate crisply, establish crab into the wind and track the centerline to 500 ft.
Get behind the weathervane effect or left turn early and you will be trimming the infield. Biggest mistake is allowing the tail to start moving. Then you get to fight inertia and wind.