If the diver is both certified & experienced in both overhead & solo, has the appropriate extra equipment (bailouts) & skill to use it, I see no problem. I know many divers who cave dive solo. Personally, I will only make a cave dive that I am comfortable with doing solo. Have I? No. But I am comfortable enough to do the dives solo if I want, or need to. A lot of my training basics was to be self- sufficient within a team, which actually makes the team stronger, if everyone is. No one is dependent upon anyone else, yet there to help, to add another layer of safety. Times when cave diving solo is actually safer? I would say in a particularly nasty system (low/ narrow/ silty), where it would be stirred up just from movement through & the 2nd guy would see nothing. Usually the diver(s) are coming out on the line. Also, at at times it may be safer in an exploratory mission, where there are many unknowns.