yes (car rental prices are mostly a function of size)
But in reality, rarely. The pricing is mostly a function of luxury AND space.
I’ve regularly seen larger cars with more capacity equal to medium sedans.
Only when you're comparing the cheapest vehicles of each size, where the cost of the vehicle and maintenance is probably roughly in line with vehicle size. There are plenty of luxury and sports cars widely available for rent that will cost more than a minivan.
different scenario; more appropriate would be the same car with zero or 1,2, or more passengers.