A much bigger problem than the lines are the switches. Switching of trolley buses at intersections is not really all that well solved of a problem as is, and the solutions available right now (up to the most sophisticated based on radio signaling) are a primary failure point, maintenance intensive, and expensive and complex enough that the cost of a four-way intersection set up for four-way electric travel is going to be pretty formidable.
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.
I'm not saying attach the overheads to the light poles, I'm saying we do things of similar scale/difficulty all the time (while we are very far from at-scale battery based transport).
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.
> Switching of trolley buses at intersections is not really all that well solved of a problem as is
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.
All this can be mitigated with a small amount of battery in the vehicle. Essentially each streetcar is a BEV with battery only to go a few miles but is essentially recharged while on street power (with software to keep SoC in the 20-90% band).
