It seems like you have concerns about the coaching decisions made by the New York Rangers and the track record of head coach Peter Laviolette. It's important to note that my knowledge cutoff is in September 2021, so I may not have the most up-to-date information on recent events. However, I can provide some general insights based on the information you provided.
Coaching decisions in professional sports can be complex and subjective, influenced by various factors such as team performance, player dynamics, and organizational goals. It's not uncommon for teams to make coaching changes based on perceived shortcomings or the desire for a new direction.
Regarding Gerard Gallant, while he may have had success in the regular season during his tenure with the Rangers, the organization may have had concerns about his ability to make necessary adjustments in the postseason or address player concerns. Sometimes coaching changes are made with the goal of finding a better fit for the team's long-term success.
As for Peter Laviolette, it's true that he has had ups and downs throughout his coaching career. Like many coaches, he has experienced periods of missing the playoffs or early playoff exits. However, it's important to consider the context of each team and season. Coaching performance can be influenced by factors such as team composition, injuries, and other variables beyond the coach's control.
The decision to hire a coach immediately after being fired can depend on a variety of factors. Sometimes coaches are sought after quickly due to their track record or perceived ability to make an immediate impact. Taking time off between jobs to reflect on changes is a personal decision that may vary among coaches.
Ultimately, coaching decisions are made based on the unique circumstances and objectives of each team. While past performance can provide insights, it's also important to consider the specific context and dynamics of the team in question.