I stand corrected (again

). 210.23(C) seems to be the limit- 50 amps. So I suspect you are running a feeder or installing 50 amp cir. I have seen other trades demand way more than what is required.
I miss those little two letter words all the time, "OR" gets me the most LOL
What code says that you can do this?
As a feeder 215 allows any size as long as the other parts are met, but remember the definition of a feeder, which will require OCPD's at the pole, and 240 will limit type of fuse OCPD's because of the 480 volt you are using, at 240 or 208 we have options of in-line fuses, but not when we exceed 300 volts between conductors, I have seen many small 4 circuit panels at poles with locks on them that allow any size feeder, but this can also limit controls to turn on just a few of sections of lights depending upon the location of where you want the controls at.
I would RFI as to if they really want a 60 amp circuit or are they just requiring minimum conductors to be #6 for voltage drop? if the latter then you have the ability to just run #6 with a 50 amp breaker protecting it, it will depend on the calculated load.
Even for a small ball park I have never ran anything less then #4's for voltage drop, as HID lights can fail often if the voltage drop for startup is too much.
As for the poles, we always ran 100 amp feeders with 60 amp 600 volt R-3 disconnects at each pole that they locked on to keep other from playing with them and turn them off, then we use a FRS 50 amp fuse in them (I think FRS) so much been on my mind lately can't remember, anyways most fields would have 3 poles on each side and the center pole would always have two racks of lights on them, so each 100 amp feeder would pick up two poles, and the center poles would have it's own 100 amp feeder and two fused disconnects, each rack of lights is about 15-1500 watt Metal halide fixtures which is about 35 amps of connected load per rack at 480 volts 3-phase, but some smaller parks can be much less.