What simple divider solution could be used? 60 is not evenly divisible into 32768.

Not simple, but possible in hardware

32768 divide by 256 = 128 which is 8 more than you need for 120Hz. So drop 8 of every 128 pulses, or 128/8=16 so every 16th pulse of the 128Hz is gated out (dropped/swallowed). This gives 120Hz.

Then divide the final output by 2 to get a 50% duty cycle at 60Hz. But this needs too much hardware... several counters and gates.

It's really way, way easier with a small micro running an internal counter and dropping the needed counts.