What you are seeing is the result of “Galvanic Corrosion”. This is a known issue and there are a number of articles that touch on the problem. In short, carbon can be better, but it is not 100% immune either. Even if you sidestep it as a problem with a bar swap, there are likely potential issues elsewhere that you may or many not have already checked as well.
In particular, if you use a carbon bar with an aluminum stem, you need to be sure to prevent sweat from contact there as well, or clean it thoroughly since the aluminum/carbon contact is an issue with GC as a result of the salt element.
The best solution is to reduce sweat accumulation if at all possible. More and/or better fans indoors, AC or other considerations. Some people wrap plastic over bars or use protectors with plastic shielding. A towel only helps hold sweat in the area, but unless you also clean and rinse the parts under that soaked towel will you get rid of the harmful sweat/salt that is the root of the issue here.