Everybody does it like that... Uh oh! This could be either:
The rules and procedures are just not adequate to get the job done safely and people fall back on their professional knowledge and experience to get the job done in lieu of following the existing procedures.
You have a problem with your safety culture. A collective agreement has been built that (these) procedures need not be followed and it has become "not done" to address this.
Well, whatever way you go you have a job to do. Either your procedures are no good, or the groupdynamic is no good, or both, so there is work to do.
When it comes to the procedures, it is important to have procedures in place that are aimed at helping professionals do their job safely and efficiently. Poor procedures, which are often drawn up by people who do not understand operations and are justified by a desire to control behaviour, are unacceptable and will actively invite violations. It is the duty of management to have good procedures in place. If safe working necessitates a loss in efficiency, make sure this is understood and agreed so that it is done consciously.
To correct procedures: own up that the procedures are bad, and invite your best experts to correct them with you, bringing them in line with professional standards. If that is not possible immediately, due to e.g. the fact that the procedures were imposed from outside, openly address this issue and seek agreement on how to deal with this. Not dealing with bad procedures will lead to a bad safety culture.
To correct the culture: Well, there are many texts, approaches and books out there to help you. The most important thing is however that you start addressing the basics of the team behaviour ("Are we here to help each other excel?" and "How have we been working lately that is not in line with how we want to work?") and to bring the team back to the shared ambition and task of the whole team (in HRO's this is often related to caring for the lives of people).