What else could be more important?
AB - I will tell you what is more important.
First the ability of emergency services to try to save the life of the person in question or other people injured in the same incident where the presence of a priest giving last rites may hamper their efforts to save lives.
Secondly where we are dealing with a crime scene and allowing a priest to access that scene may contaminate evidence making it unusable in a trial that would potentially convict a dangerous criminal and also provide justice for the victim's family.
Both are more important. But as I've said previously these would be very rare situations so in the vast, vast majority of cases there will be no issue with a priest being able to administer the last rites, providing that the person consents to receive them.