He got chances in preseason as a rookie.
2015, Preseason Week 1, New England: 2 for 14 yards
2015, Preseason Week 2, Pittsburgh: 1 for 10 yards
And that was that unless he had fair catches or no-touch snaps in other games. Janis and then Abbrederis took over starting in the second half of that Week 2 game. In 2016 preseason it was Abbrederis, Davis and Hyde. In 2017 preseason it was Davis, McCaffrey and Rollins.
I checked out the tape on those 2015 Montgomery returns using espn.com's play-by-play to get the play times and then the NFL Game Pass tape archive to view them.
In the Week 1 game, in addition to the 2 returns, he had 2 fair catches and there were 2 other sideline kicks with a lot of air under them where he let the ball hit the ground instead of coming up to fair catch. Not coming up to fair catch is a pet peeve of mine with Davis as well. It's dangerous, it takes balls, but it's part of the job.
In the Week 2 game, on the one return, he misjudged it a little and stumbled getting started. He had a lot of free run to get 10 yards. In addition to the 1 return, he let a sideline line drive ball hit at the 5 which was downed at the 1, followed by a safety. The decision was not unreasonable. After that, Janis took over in the second half.
Here are my impressions of Montgomery fielding punts:
He does not look natural doing it. A couple of the punts he caught hands up toward the face. Then there's that misjudged ball in Week 2. It looks like he has trouble judging the ball flight. This is consistent with his college tape as a receiver which showed poor tracking and adjustment to deep balls. Letting a couple of catchable balls hit the ground may be less business decisions (which may be Davis' problem) and more misjudging ball flight.
Davis is a much more natural fielder of the football. If you want to displace him, the best candidate who shows natural tracking and fielding of the football and elusiveness in his gitalong can be found at the 1:38 mark in the following tape:
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I wouldn't risk it, though.