Is there any reason that other theme elements (such as nav menus) shouldn’t be within the loop?

  1. If you do this on archive pages you will get a lot of duplication
  2. You can have trouble if one of those elements alters or overwrites $wp_query or $post or any number of other things

Keep your page structure clean and logical. What you are asking is something like “Is there any problem with putting my underwear on over my pants?” Well, you might get it to work, but it is odd, your underwear isn’t really doings its job anymore, and your friends and family may start to mysteriously pass on diner invitations.