Don't know about later gen Priuses, but the first gen and second gen definitely use a DC-DC converter to charge the 12V. However, perhaps this is inactive when the car is off. The HV battery is not very big (a few kWh), and the 12V battery could be worn out too.
Most cars with traction batteries use an alternator, do maybe they switched at some point. While less efficient it's cheaper. It's a shame they need a 12v battery at all (even EVs have them, despite not hanging a starter motor) but there is so much invested in the 12v system they can't just ditch it or redesign so many components and systems.
It's not there for fun, or because of the legacy 12V systems, but rather safety.
In any serious accident requiring the airbags to be inflated, electric vehicles are required to trip a pyro fuse which disconnects the HV from the vehicle systems. The battery is fully isolated and floating from the 12V and chassis normally but this will also disconnect HV from the motor etc. This makes it much safer for first responders as they do not need to worry about cutting through high voltage cabling (in the Model S, the 400 VDC power for the air conditioning system runs along the side of the passenger's door frame, which could be easily broken by a jaw-of-life on that part of the car.)
But, if you disconnect the HV, how do you power hazard lights, airbags, doors, etc in a crash situation? The 12V provides this power.
I am certain in a few years Tesla and other EV manufacturers will replace the lead acid 12V with a lithium type, possibly LiFePO4 because of its greater tolerance of deep discharge and safety (the 12V battery is much more exposed and at risk of being punctured in the most severe accidents.)
It's also likely that as semiconductor switches replace relays in car systems vehicles will move to a 36~48V DC bus.
You are assuming they have a free choice of placement. Where in the world can local government build anything it likes anywhere it wants?
This
isn't a good argument for putting solar on the road surface though, which is quite frankly a ridiculous idea for many reasons. The embankments alongside many motorways would be an ideal place to install solar generation, if you insist on putting it along existing roads. Whilst the local authority may not own the land (I can't find any information on how much land they own beyond a road's tarmac, if any) I'd argue the land would have little expense given that it is unsuitable for nearly anything else.