As someone who is familiar with (but didn't work directly on) military laser systems, the devil is in the details
The energy put into the target depends on the surface area (SA) being illuminated times the power per unit area. It also depends on the ability of that material to absorb energy at the wavelength(s) it is being hit
Fiber optic cables are fairly small SA and tend to be made out of materials that are really good at not absorbing light. Lasers would need a really, really long time to put enough energy in to make something happen if at all.
The other thing you need for any weapon system is target acquisition and tracking. For laser systems this is very important as you want to keep heating the same bit of the target (shaky aim is bad). Drones are hard to target via electromagnetic or sonic means. Since lasers systems require more precise targeting you are playing to your weaknesses here.
It would be easier (though not easy) to target the drone vs. the FO line unless you knew where the FO line was coming from on the ground (in which case you would just call counterbattery fire on the source and not worry about the stuff in this post).