+1

Having said that, there are merits to both driving and train. As others have said, it might be better to go point to point by train and then hire a car to drive locally.

Personally I prefer trains in Japan. But of course there are certain areas where a car comes in handy. Also, one of the joys of highway driving for me are the service/parking areas. They are amazing. Some even have ferris wheels and onsen. Gift shops are cool, and you can get some amazing "B-kyu gurume". I once saw on TV an SA that has an aquarium. On some summer weekends, though, SA/PA's can be downright hellish with too many people.

Cost-wise, it is probably a bit cheaper for 2 people to go by car to go from Tokyo to Osaka/Fukuoka than it is to take the bullet train. For 3 or more people, the car is MUCH cheaper. Even without the ETC discount, Tokyo to Osaka would be ~12,000y. Assuming 10km/L and 170y/L, gas would be 8500y. So ~20,000y plus whatever the cost of the car rental is. Shinkansen from Tokyo to Osaka is ~27,000y for two people, ~40,000y for three. Of course that could be mitigated to some extent by discounts from Jpn Rail Pass. Even then, driving is generally cheaper than train for long-distance travel in Jpn involving multiple people, even when you consider the high cost of expressway tolls there.