Concorde, when it was acelaring through transonic speeds had to do a
large fuel xfer to the aft tanks to conpensate for the strong nose
down trim shift.

It was rumoured to be certified

I've already written about this : in a supercritical airfoil (read
supersonic design) the Aerodynamic center does move back as the speed goes
ABOVE MACH 1.
Also, delta-wings tend to be challenging to manage in terms of CofG, so,
they usually require some form of fuel xfr to keep'em in balance.
Classic example is the british Vulcan bomber, that required substantial
amounts of weight (30 tons come to mind) just to be in balance...

So these will become issues when we start flying supersonic gliders with
delta-wings...
Maybe the space-shuttle pilots out there can share their views.