Trams and busses and trains have been running off overhead lines for a long time, so it clearly works.
The main issues are that it doesn't obviously scale up (i.e. it works fine for a few trams, but not necessarily for thousands of cars filled with 1-2 occupants each) and it would be very expensive to roll out widely. Especially for last mile transport, where it basically becomes infeasible. There's just too much road.
Essentially, it is a viable alternative, but only where public transport is the major form of transportation. If people are still driving thousands of cars rather than taking the bus then it's impractical.
Ground level power supply systems also exist[2], but would require you to tear up the entire road network in order to implement them, are expensive, and apparently prone to water clogging (which could perhaps be mitigated) without mentioning the fact that they would probably require either an autonomous or guided vehicle in order to reliably maintain contact with the rail.
So, not really, the limitations are mostly about cost and political capital.
[1]https://www.siemens.com/global/en/home/products/mobility/roa...
[2]http://www.alstom.com/products-services/product-catalogue/ra...
Gaps in the wire for intersections and underpasses could be handled by having small battery packs in the cars. This also helps with the last-mile -- only large arterial roads need to be electrified and cars could drive the short distance on city streets on battery power.
One solution for in-road charging would be wireless inductive chargers like:
https://www.cnet.com/roadshow/news/qualcomms-inductive-charg...
Though as you say, the real problems are price and politics. In the SF Bay Area, Caltrain has taken decades to get funding for electrification and has faced a lot of resistance from some communities for the construction and visual blight of overhead electrification. And that's just for one set of tracks, electrifying all of the freeways would be much worse.
Like I said, it is technologically possible, but for most intents and purposes seems like a wonky solution, at least for personal vehicles, mass transportation and freight are completely different scenarios.
As for the other points, you are right, there are fairly straight forward solutions.
Inductive charging is definitely a good option, which has already been explored by transport companies[1]. It again seems to be that politics and money are the main barrier for implementation.
1. It's expensive, and that cost doesn't work out when you have petroleum available as a fuel and can just carry your own energy supply around easily in a small tank under the passenger compartment. It probably still doesn't work out when you have coal, or coal-derived diesel, or vegetable-derived diesel, or "good enough" batteries, available, because those systems are simpler and don't have the funding problems (most of the cost is shifted to the user of the vehicle, which prevents the politically crippling cost of a public system).
2. When you finally designed a system, and standardized the vehicle heights and worked out all the other issues, I suspect you'd have reinvented electric trains. (Or some sort of essentially train-like system, or a system that's not advantageous enough over trains to warrant building it.)
Basically it's an idea that's pinched between existing technologies that are good enough in their current forms, and has an extremely high implementation cost. The risk-factored ROI just doesn't appear to be there.
https://www.geek.com/tech/musk-shares-first-image-of-boring-...
People are really underestimating the impact of lower cost tunneling.