Does a bike helmet without chin straps make any sense? Wouldn't any major impact make it fly off the head and not protect you.
Yes.  And no.  It makes some sense in that a helmet should fit snug enough to stay on on its own.  The chin strap's job it to keep the helmet on your head after the initial impact.  Were one to have some condition (a skin condition, stitches on the face or neck, etc) where the chin strap was extremely detrimental, one would be somewhat safer riding with a helmet simply missing the chin strap, than with no helmet at all.  

However, barring some obvious condition, or a radical helmet design that doesn't require a strap to stay on after impact, a helmet without a chin strap makes no sense.