I moved a bunch of sheet goods with my Civic coupe, by which I mean I moved sheet goods on a bunch of occasions, one or two each time. The problem comes out to be weight, and ease of loading/driving.
The real solution for moving larger things is a trailer. UHaul rents trailers for the occasional use ~$20/day, no mileage charge. I say occasional use because it takes effort to go and get it, and UHaul builds them like brick shithouses. So you can get a lighter one that's nicer to tow if you buy one for a few kilobucks.
I inherited a light crossover SUV that's more than capable of towing a 5x10 trailer with a modest amount of weight around town. It does highways too, but keeping ~65 rather than ~80. If I were still limited to the Civic and needed to move stuff on the regular, I'd buy an even lighter trailer.
And a trailer has very little maintenance compared to getting another motor vehicle. I've started bringing a pallet or two and putting them down under whatever I get so I can just fork stuff off at home (and then in the case of stuff from big box stores, fork the rejects right back on to get returned).
These Kei trucks look neat, but I don't think they would actually solve many problems I have. A dump bed would be fantastic, but if I really needed that I could just bite the supply shortage bullet and get a dump trailer.