Why can't generators with different frequencies supply the same transmission line?
Equipment designed to work with one frequency power will not necessarily work with another frequency. 


Transformers designed to work with 60Hz will have lower ratings when working at 50Hz (Important for power distribution and individual devices)
The speed (RPM) of AC motors is tied directly to the power line frequency.
AC Wall clocks wouldn't work :)


The combination of 50Hz and 60Hz would cause generators to fight eachother


See the plot of both 50Hz and 60Hz superimposed from Wolfram
The blue plot shows the difference. Where the function is large, the generators are fighting eachother (Big Boom!)