Airborne Laser on a nuke powered plane at Mach 5.5

Hell, I am supposed to stop these speculations.  But this will be another speculation alert anyway.  Wtf.

The Airborne Laser was under development for over a decade.  It had reached the point was it could have been made operational, but was deemed to be too expensive and too vulnerable to be useful.  So, it was canceled.

So, I was wondering about that.  What if you made it faster and could fly higher?  In the Apollo Era, there was this supersonic bomber program that involved a plane that could fly at Mach 3+ and could operate at 70k feet.  Those too were deemed to be vulnerable.  But what about a plane that could fly at Mach 5.5?  Yeah, I'm thinking the concepts borrowed from the Skylon.  A faster plane can outrun an air defense.

Let's go even further and put a nuclear reactor on board.  It then could fly around the enemy's backyard indefinitely and they'd have to figure out a way to shoot it down.  Not easy to shoot down a plane that can outfly a missile.

Not only could it outfly the missile, it could shoot it down.  Put a fleet of these things in the enemy's airspace and watch them deplete their missile batteries trying to shoot the rascal down.  Then if they launched a nuke, you could shoot that down too.

I know this all sounds crazy, but who said you can't do it?  There was a airborne reactor experiment that produced a successful engine.  Now, if you add a precooler to it, it could go up to Mach 5.5.  In fact, since you don't need to carry fuel, you could have a lot more cargo area that could be used for the lasing equipment.  It could stay aloft indefinitely.  Shielding?  It wouldn't need any since the thing could be flown by remote control.