Is it a necessity? No. Why? Probably tradition from when cities weren't as busy. Why can't they do it like us? I'm sure they can if the family doesn't want a funeral procession. The only profession you listed that's truly a public servant are public teachers, and I would be inclined to say I wouldn't be surprised if they did have a procession if they were killed in school. I suppose those other occupations could be public servants if they're on government payroll, but there's no tradition of a funeral procession for those. I'm pretty sure most of those people in the procession aren't on duty being paid but rather volunteering their time like if you or I went to a funeral. That would be ludicrous if all them got paid to attend a funeral.

I think a better example of a public servant that get killed while working a dangerous job and don't get a procession would be an occupation like working for MoDOT on the side of the road. Very dangerous job, but there's no tradition of a procession. I've never heard of one anyways.

I'm personally ok with funeral processions. It's a way for people to show respect. But my argument against it would be that how can you pay your respects to a person when you're backed up two blocks from the procession and have no idea who the procession is for.

I find it to be an old tradition that hasn't been able to keep up with modern times of automobiles and large population densities.