It doesn't help that most car manufacturers use locked battery charging protocols that don't allow you to easily change this process.
AFAIK other car makers in the US use either CCS or ChaDeMo.
In Europe, all car makers (including Tesla) support CCS.
CCS allows DC charging and has support for load balancing, so I assume it could be feasible to create a home CCS charger that directly charges an EV with DC from solar panels.
However, considering how expensive power electronics are, and how difficult it would be to integrate such a charger into an existing solar installation, I have doubts that many people would buy such a charger. Also, I don't really know how CCS works in detail, so I may be totally wrong about this.
In fact, many cabin installations don't even use inverters to convert into AC. They instead use DC appliances. So no, going through AC makes no sense in this scenario.
As for DC voltage levels, that of course is dependent on solar panel configuration and battery cells configurations/packing. Virtually all electric cars have a built in charger with a switching power supply that's already doing the DC voltage conversion. What I was remarking was that there is a lot of duplicate electronics that perform the same function and that a lot of intermediary steps can be eliminated.
That isn't what you would do for anything tied to the grid. This is far more common (economies of scale mean the parts are cheaper). There you would take advantage of AC's ability to change voltage easily to allow the panels to be farther from the rest of the system. You would also want to use the grid as a backup for any system failures in the solar setup.
Eliminating steps isn't always a good idea.