I understand that the tire speed on take off of the Concord is much higher than other planes, but I still would think that a burst tire at take off or landing would be a bad thing.

While on sub-sonic planes it may not be fast enough to puncture the wing, but would it not have a negative effect on overal control of the aircraft - even at the slower speed?

If you think about the planes like the F100, S80, etc. where it's a single wheel under each wing, a blowout on takeoff and landing seems like it would present a loss of control and become quite dangerous.