What do you really expect out of a 7th round selection? Lac Edwards did some things well in 2016 and he also struggled at times. He's certainly no Johnny Heckker or Marquette King (Who i wanted the Jets to draft a couple of years ago), but he's a young man still finding his way.
Edwards finished the year with 75 punts for 3,236 yards. Unfortunately that only equates to a 43.1 yard average which was good for 28th best in the league. He did manage to place 24 punts inside the 20 yard line (17th best in the league) and force 22 fair catches (11th in the league).
Edwards did have one punt blocked against Miami that resulted in a TD, but I don't think you can blame that on Lac. Rookie running back Brandon Wilds forgot to block his man and Walt Aikens had a clear run at Edwards. However his fumbled punt and poor attempt to recover the ball against Baltimore that resulted in the Jets falling 7-0 behind was definitely on him. He had some stinkers just in terms of punting as well, the week 4 games against Seattle comes to mind, a game where he punted 5 times and averaged just 39.4 yards.
I imagine the Jets will bring in competition for Edwards through camp, he's didn't show enough in year one to be handed the job, and as a 7th round selection, if he gets outplayed by someone else, the Jets can easily cut ties with him. We don't know what the offense is going to look like, but it may be an idea to try and sign a punter with a bigger leg than Edwards, his long in 2016 was 59 yards...good for 29th in the league.
You have to consider the unit as a whole when looking at punters or kickers, the coverage on punts and kicks goes a long way to determining how effective they are. The Jets may have allowed a kick return for a touchdown, but they managed to avoid allowing a punt return.