Just to clarify--the candidates for the NYPD Stakeout Squad (which incidentally, was not a "surveillance team") were New York City police officers. Their work experience was known to the Department.
Jim Cirillo was charged with the responsibility of selecting and leading the team. It was his responsibility to choose from the candidates. It seems that he was quite successful at that.
The duties of the team differed very significantly from what a civilian defender would be expected to do. However, some of the attributes that would support success on that team would be helpful in self defense.
Of the ones mentioned in the interview questions, performance under pressure would be foremost, along with the aspects of firearms skills that the questions about competition might bring out.
The OP pointed out the differences between running around with a timer shooting at targets known in advance, and dealing with completely unexpected threats materializing from different angles. That's important to the civilian defender.
The Stakeout Squad did neither of those things.
They located themselves behind cover and concealment and awaited the entry, through doors, of criminals whose arrival was considered likely. They did not move around, and they did not work as individuals. They were very heavily armed.
The matter of whether real real world experience is sufficient or even very helpful, either to the defender or to the instructor, has been discussed here at great length over the years. The fact is, there are far too many variables that will never manifest themselves in even a large number of incidents. The same thing manifests itself in air combat. The development of sufficient numbers of strategies and the development of sufficient skills simply does not and cannot occur in real combat. For that reason, simulation and real FoF flight training is used.
When it comes to defensive firearms training and skills development, far, far more can be taught, experienced, evaluated, and learned in several days in FoF simulation in a shoot house or parking lots than any one person will ever see in a lifetime. And it is possible to separate out the effects of random chance.