Umm, at what point was he rushed and bounced too much between the two leagues?
Rookie pro season he was recalled twice, first time for 2 days and second time for 10 days. Didn't play any NHL games, but played a respectable 41 AHL games.
Second season he was again recalled twice, first time for 3 days and second time for 38 days. IIRC this was the time when Lu got injured, Reimer was healthy and vice versa. Montembeault started off well, but again his inconsistency showed, but that is to be expected with young goalies in their first NHL games. Despite spending over a month with the big team, he again played a very respectable 39 AHL games.
Third season everyone expected him to make the team, which he did, despite a poor showing at training camp (at least from what I recall). He stuck around until the end of November, odds are he doesn't get recalled unless Bob and Driedger get hurt. 1 day, 7 days and 47 days call-ups in January - March.
Fourth season not much to talk about, since covid messed up everything on most AHL teams.
I'll give you the third season that Monty didn't get to play enough AHL games, but the amount of NHL games certainly wasn't too much to ask from him and the stints he had in years 1&2 were fine. Eventually you have to start phasing in goalie prospects, sometimes it's through choice and sometimes you're forced to. I would blame our AHL coaching if anything, since Monty still had the same consistency issues in pro year 3 as he did in juniors when we drafted him.