I've been playing headless basses for 30 years. I see no real big cons in a headless bass. I own an '88 Steinberger XL-2, I've owned a 4-string and a 5-string Steinberger Synapse. I just bought an NS Design WAV4. The only headless bass I've had that has been an issue is a Steinberger Spirit XT-25. It's a cheap replica of a Steinberger built by Epiphone, and the problem with it isn't that it's headless. The problem is everything else.
The new tuning system that Ned Steinberger has developed (Check out thinkns.com.) takes any regular string, but it has to be used with the adapter that he designed for the end of the neck, which is where the single ball is inserted. I don't play headless basses exclusively, but I sure do like the ones I play. And I have no affiliation--past, present, or probably future--with Steinberger or NS Design.