Further, electric lines exist mostly on shared poles. For safety reasons, shared poles require a buffer space between MV and distribution voltage power lines and communications lines. This means that the typically 600 VDC trolley bus power cannot be added at the level of communications lines (well, can be with some work, but in practice it is expensive and complex) without compromising this safety buffer, requiring deenergization when communications utility work is underway. In many cases they cannot be near communications cables even if communications work is prohibited when the system is energized, because of the risk of inadvertent contact putting 600VDC on coaxial or telephone lines which could create fatal situations. Additional expense is required to mitigate this problem.
Trolley lines also have more complex physical loading requirements than power lines because they must cope with the lateral forces of vehicles, so they usually need to be anchored to both sides of the street on crosswires, to poles that were engineered for that use. Most of the time attaching trolley lines to existing poles will not be feasible for these reasons and they will need to either go on dedicated supports, be attached to buildings (the engineering and real estate paperwork for this is complex), or have existing poles replaced with ones engineered to support trolley lines as well.
Like the parent comment said, it would be a hybrid able to use battery power when not on the line. With this type of system you could then just run parallel lines instead of criss-crossing lines.
Batteries are fun and all, but they are way harder to deal with vs. anything you described; they're just earlier in the development curve, so the problems seem more solvable.
It only seems like a daunting problem on roads because we don't already do it.