In large city cores, most car parking is underground or in big garages as surface level parking is too valuable. In industrial parks and such, parking is usually in open lots surrounding the buildings.
There is another issue with solar panels, they need to be kept clean or their efficiency drops. Road conditions are among the grittiest around. The need to keep the panels clean requires more water. Most professional car washes today recycle water, but people washing cars at home usually let the water flow into the storm drain. If you take your solar powered car to the professional car wash every day, that will save more water over washing it yourself, but it is an extra expense of $5-$10 a day as well as extra time you have to take out of your day to do it.
Of the technologies that will almost certainly come down the pike in the next 10 years, battery concentration is probably the easiest. The current batteries used in the Tesla are a commercially available cell that is not that space efficient. Redesigning the individual cells to fit into the available space will probably allow an 85KW battery to get about 30-40% smaller. That's simply an engineering and manufacturing job, no scientific breakthrough needed.
We might see a new battery technology that is better than lithium ion, but that's more dependent on the science, which is less predictable.
For some situations, a car rooftop solar array might be of some use, but I don't think it will ever catch on as a mainstream product. We'll see what happens. The nature of science is such that we can make some predictions based on technologies in the lab today, and we can dream about technologies that are being researched, but some technologies have proven to be elusive, even with a lot of R&D. We've been trying to do hot fusion since the 1950s. We can make very short fusion reactions, which are very destructive (nuclear weapons), but we have yet to have much success with sustained reactions that would be useful for energy production.
Bill