I don't think that is necessarily silly to work out to look and feel good. But like others said, it is fruitless to work toward an unattainable goal. In a perfect world, yeah maybe I'd have a tiny waist, but unless I remove a couple ribs (nope!!) or take other drastic measures it's not gonna happen naturally as its just not in my genetic makeup/body shape. It's almost like training to be a foot taller...
So yes I'm sure you can jog and train and that will tighten things up, but having already been to an unhealthy weight without seeing the gap, I think it might be more realistic to focus on more attainable goals. E.g. If you work your legs overall, I bet ya people will be more astounded by your killer quads/hamstrings and never notice a lack of gap.