I wasn't alive in 83 but I'm guessing the time on the clock was less than 15 minutes. That's another thing that bugs me. These teams have a board and have to have a really good idea who they are taking. Granted yeah it depends on what the team in front of them do but it usually plays out unless a team makes a random pick. Teams milk that 15 for every damn second. I guess that's their right but again I have a hard time thinking they don't have their minds made up before the day.
The 15 minutes was overkill, but at least they've reduced it down to 10. Part of it was the poker game. Teams used up their allotted time just in case a trade scenario did pop up.
http://espn.go.com/nfldraft/columnist?id=1545117
There was a comical instance where Dallas and Kansas City were working out a trade and it didn't get completed until the 15 minutes were up. So Minnesota could have snuck in and made their pick, but they hesitated for a minute and DAL/KC got the paperwork in. Minnesota missed out on their preferred target (albeit they probably lucked into the better player).
Then the next year, Minnesota went over its allotted time and the next three teams made their picks immediately. Minnesota ended up with a tremendous guy in Kevin Williams but it didn't make their front office look good. But to your point, teams for the most part will know who they're picking but there's no penalty in taking your time. Plus in the first round, the TV broadcast will want a couple minutes to interview the players plus the time for photos/etc.
In 2004, I believe AJ Smith called Ernie Accorsi halfway through the Giants' 15 minute window. They found some common ground but couldn't hammer out a deal in 7 minutes. So the Giants ended up drafting Rivers and then finalized the trade a few minutes after that.
There's just something about drafts that I enjoy. I'm not even a big basketball fan and I've attended an NBA Draft.
One random clip I wish I could find was when the 49ers traded up for J.J. Stokes in 1995. Memory is fuzzy, but I seem to recall the crowd going into stunned silence like it was unfair that the Niners (a couple months removed from the Super Bowl win) were snatching up a premium talent.