If you think Penny is the character you're supposed to identify with, then we're not watching the same show.
Penny is obviously hot and has social skills but she's also ... well ... not the sharpest tool in the shed. And the show makes that obvious. Leonard is the clear main character in this show, being nerdy but not so much that he has no clue what he's supposed to do.
He's just not very good at it sometimes, because he gets nervous, which i think most anyone can relate to.
What TBBT actually is is Commedia dell'arte, just like most other sitcoms.
The idea is you have a cast of caricatured characters. The characters are not, for the most part, deep. They vary in extreme ways in terms of their personality so that they're readily identifiable from eachother and from non-central characters. They are deliberately written to be abnormal - again, caricatures.
So you take these characters whose extreme personalities will dictate their reactions to things and plonk them into a scenario. Any normal person who has to achieve a basic goal - asking out a girl, for instance - would be boring to watch. They'll achieve or fail with zero antiques. But these caricatures are incapable of handling real world scenarios and the resulting fallacies & drama is entertaining.
The only difference between Seinfield, TBBT and Friends is TBBT uses 2000's and 'nerd' culture as it's central theme rather than 'jews' or 'twenty somethings in new york in the 90's'.