I find that the aspect ratio fits narrative action better and gives the characters more room to move. I was reminded of this a little while ago, before I was even shooting with anamorphic lenses, when a client came in asking for interviews shot at 4:3 rather than the usual 16:9. I used to shoot 4:3 all the time, but it was weird going back and it was difficult to frame the subjects in a way that I felt good about. Now I feel the same way shooting in 16:9 during my day job rather than 2.35:1 or 2.55:1.
I think that for most people like myself who go through the trouble of shooting with anamorphic lenses, it's less about aspect ratio and more about aesthetic. There's simply nothing else that looks quite like it (well, Rich's FlareFactory lenses do come pretty darn close but I don't think of them as anamorphic; they are something else entirely). Not everyone will be able to tell the difference between spherical footage and anamorphic footage. But for me, once I was able to spot it, I was hooked.
Also, I certainly don't mind the ability to shoot at higher resolutions while taking up less card/disk space.