With CDL, the key word is COMMERCIAL. The Federal Gov't created a bunch of CDL requirements they pushed out to the states years ago in order to standardize requirements for interstate commercial trucking.
As mentioned earlier, I've never heard that any state requires a COMMERCIAL Drivers License in order to tow any weight RV for personal use. Chris, you seem to think otherwise, but I doubt you can back that up by pointing to a statute.
Some states do require a NON-COMMERCIAL class A license when towing an RV over a certain weight, even for personal use. California is one. Texas is another. Neither enforces the requirement. Would there be some legal liability if you cause an accident in your home state and don't have the required license? Maybe. My thought is that the legal exposure would be to a claim of depraved indifference which could remove pain and suffering liability caps such as exist in Texas. But I'm not a lawyer - so who knows.
And we have in the past had extensive discussion about whether a state you visit will honor your home state drivers license, based on the laws of your home state. A number of people with many years of law enforcement experience weighed in on those past discussions to say that there is reciprocity and your home state's license authorizations will be recognized by law enforcement in the states you visit. Clearly, if they didn't do so, it would be rather chaotic.