You're describing CT!!

  A character with STR 2 is not handicapped.  He's a weak person, physically.  I liken STR 2 with the character Jeremy Davies played in 
Saving Private Ryan.  He doesn't have some disease that withers his muscles, he's just a slight fellow. And, he sure has heck won't be winning any Ultimate Fighting Championships, either.
 
If you flip through Supplement 12 Veterans, or Supplement 1 1001 Characters, you'll see characters with "2" stats.  And, they're all viable characters--not wheelchair bound or anything.
 
As for the disconnect, this is one of the things that I love about CT:  It allows you to deal with those issues.  Vacc Suit-1 doesn't always mean a +1 DM.  It can mean a lot of things...or nothing.  The same with stats.  They can provide modifiers to throws or not even be referenced.  It just depends on the throw.