I am building a new helicopter. I can set the cyclic servos to either 1520µs or 760µs center pulse. I understand 1520µs center pulse limits the frequency to 333Hz, whereas 760µs allows for higher frequencies of 560Hz and even higher. Of course, I can just leave the cyclic servos at 1520µs center pulse like I've done for years. At the same time, it does not cost me anything to program the cyclic servos to 760µs center pulse, except for the few minutes it takes to do so.

The ability to use 560Hz frequency with the cyclic servos set to 760µs center pulse seems like an advantage. After all, 760µs center pulse has been the de-facto standard for rudder servos for over 10 years.

1) Is there any specific reason(s) to keep the cyclic servos at 1520µs center pulse?

2) Is there any specific reason(s) to not set the cyclic servos to 760µs center pulse?

As you correctly concluded shorter pulses allows for higher frequency. This is because the longer pulses at high frequency get too close together to be read reliably, and eventually you reach 100% duty cycle so you can't physically update faster. The trade off to using shorter pulses is the narrower pwm band, with 760 you typically lose half your resolution (each step must be twice as big to achieve the same travel).

If you try to manually control servos by setting the pulse length (such as using the center trims in Spirit config) you'll likely see many servos don't even respond to 1-2μs changes, so you wouldn't really lose anything by going to 760. Only servos I've used that really have 1μs precision at 1520 center are Theta. You can try it with yours and see if you would lose any precision. If not there is really no downside, except servos potentially getting hotter and wearing out faster especially if you have any vibration issues.

However the advantage of 560hz would also be negligible if the fbl isn't making adjustments that fast. You would get some decreased latency on your input, basically one millisecond improvement at best if coming from 333. The serial receiver protocol update rate and fbl processing time contribute to latency so much more I don't even believe this would be noticeable, but placebo effect is strong.

Generally the tail servo on a heli needs to work much harder with constant adjustments, and are often made to have a smaller range of travel, so the benefit of higher frequency is much more obvious there.

the range I think it's different
for servo 1520
1000 usec min stick / 1520usec center stick / 2000usec max stick
+ or - positive and negative throw is 700


for servo 760 the range is different
760 center stick and min e max it is not 1000 and 2000
I don't remember the exact numbers but if I remember correctly for servo 760 the range is :
610usec min stick / 760 usec center stick /910usec max stick
+ or - positive and negative throw is 150

the range usec is different