I have a Lexus RX 350. The MANUAL specifically says that it should not be towed except on a trailer - all 4 wheels off the ground. No idea why. I can understand why to not tow with 4 down and I'm sure the addition of a transmission pump would void any warranty. We use a tow dolly. No issues. Have to rotate the tires a little more often to keep the wear even.
My son also has a 2001 VW Jetta. We took that to Yellowstone a while back to save the 1000 pounds when towing in the mountains. The only issue with the Jetta was the low ground clearance. Getting it on the dolly was an issue because of the bottom air dam. The dolly "helped" me get that off. After a few 4 letter words I got the remainder off and put it in the trunk. Put it back on after we got back
In either case I see no other reason not to tow on a dolly.