Nah, no rivalry, though there may be some since we originally lost Cecil to Oceana.
I doubt Charlotte will be able to support a 3rd pro team. Las Vegas needs one and can easily support far more so than Charlotte can.
HR has the population but it did the exact opposite of Jacksonville. Instead of consolidating, it remained in 7 large pieces. These 7 local governments fight each other for everything. With that kind of hurdle to jump over, sports associations would prefer not to have to deal with all that.
That goes for many things that all lead to HR not getting the same recognition as MSA's of similar size.