Why not? You just used logic to connect a ban on texting and driving to DUI, and thus justified a ban on texting and driving.
Your stronger argument is that driving is not enumerated as an inalienable right, thus not afforded the same protections as RKBA.
However, if it's not permissible to restrict an entire class of weapons in the general use, it seems likely it would be permissible to require education and training also in the general use.
Even voting has some theoretically required training for its general use. Every state's curriculum has some form of civics classes. Immigrants who miss these classes being out of the country at the time they WOULD have taken them have civics requirements in their citizenship process.