It is actually GVW being 26001 and over that needs a CDL. That is why you don't need a CDL to drive the 24 foot Ryder/Uhaul box trucks. They make sure they stay just under the 26000 mark. I believe that is the nation wide law.
my one dump truck has a 30,000 lbs plate and I have to have CDL
other had a 26,000 so not needed (EXCEPT) we pulled a tri axle trailer with backhoe or bulldozer and because of combined combo over 26,000 had to have one with it too
My guess an old truck converted would weigh in the 12 - 15K lbs depending on size and type bed so you could still haul any car and be under the 26K LBS
The other cost is the plates and insurance
Now if you can run a farm plate i think you can get by without a CDL
really a trailer is more cost effective, love my trailer and will be loading it up in just a few hours