Java, I have not heard about someone renting a toad. The people that rent cars usually rent when they reach their destination and those maintain that it is a lot cheaper than buying another car. If the trip did not include long stays at a particular stop, the alternatives would be (1) rent often, or (2) rent once and tow it on a dolly.
Normally your insurance covers rental cars. What I don't know is if the rental car companies have any issues with their cars being towed.
I looked into renting a dolly at one time and they were expensive to rent because of the theft rate. If you intend to do this often it might pay for you to buy your own tow dolly. Cost is approx $2000 and up.
Just my opinion, others may vary.
2015 Jayco Seneca 36 FK
2016 Jeep Wrangler Unlimited tow
2010 Tiffin RED 36 QSA - gone
2011 Monaco Monarch class A - gone