Stuck_in_an_ATR
...What was the reason for the Concorde to climb that close to Vmo?...
Fuel efficiency.
Very broadly, over much (not all) of Concorde's flight envelope, increasing speed meant decreasing total drag hence better fuel efficiency.
Fuel efficiency in Concorde could be summed up in these words:
"Fly as fast as you can, as quickly as you can, for as long as you can."
...Sounds a bit tricky to ride the barber's pole at all times!...
At first, it was! Then, with practice and a better understanding of the flight envelope, it became a lot easier and not as difficult as it might seem.
I would be the first to admit that some could do it better than others!