No REMAKEs. Was a Great Show really great and Theme Song is Incredible.
Remake My Mother the Car or It's about Time don't remake shows that are already great.
My Mother the Car? WOW, can't believe I even wasted space on that.
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If you are looking for wisdom here, you are going to be disappointed.

Just found a post in another thread referencing the TV pilot! It was 1989!

Yes, thanks for pointing that out. It was a TV movie in 1989, and Blake Edwards both wrote and directed it.
As pointed out by several on this thread already, how do you recreate the mystique of the original classic?? Totally impossible.

As a matter of fact it was remade!I remember ABC doing a pilot movie starring Peter Strauss! As I remember, this had to be circa '78-80.It probably was a mid-summer replacement.

Yes, after thinking about it some more, and referencing all the contributing factors you've listed, this show is probably one of the worst choices ever to try and remake.

I agree.
Peter Gunn
is about a culture of a time and a place that has vanished from the face of the earth. L.A. is still there, but it's a different city. Those smoky bars are gone. Beatnicks are gone. Downtowns have been replaced by malls, and street culture, such as it can be called, has changed. Even the word streetwise is somewhat anachronistic these days. Color would ruin it anyway. Remaking
Peter Gunn
is a bad idea. I find it a sad commentary on contemporary life and, especially, the arts, specifically film and television, that there's little that's new that's also original, really capture's
our time
in wonderful, entertaining, smart and stylish ways.
Peter Gunn
was but one of many shows that did that for its era.

Shut up about that!
We don't need these classic shows to be remade.

Most, if not all remakes, have been terrible.
It would be even harder to get the retro feel and vibe of the original Peter Gunn series. It was very unique.
I would rate the odds of a viable remake as extremely low.