Not facing who you just drafted against would be absolutely horrible. Magic sets are designed with draft in mind, and the draft tournament structure takes advantage of the rotating aspect of the draft portion. When you see your 14 potential picks, you know that a number of them are coming back to you and you get to pick another one later. You also know that every card you don't pick is potentially going to be in one of your opponent's decks.
Being aware of what's opened in a draft as well as what's being passed has an impact on how you pick (for example: tons of red cards keep going by - table isn't into red, so you can A) wheel red cards easier, and B) bank on not running into a hyper aggressive deck and build accordingly). If you were thrown into a match against someone who didn't draft at your table, they might have a deck that wasn't supported by the collective pool opened at your table and you'll be caught completely off guard.
Being aware of what's opened in a draft as well as what's being passed has an impact on how you pick (for example: tons of red cards keep going by - table isn't into red, so you can A) wheel red cards easier, and B) bank on not running into a hyper aggressive deck and build accordingly). If you were thrown into a match against someone who didn't draft at your table, they might have a deck that wasn't supported by the collective pool opened at your table and you'll be caught completely off guard.