Well, considering that altitudes above FL1000 have been, for the last 60-odd years, considered to be outside the FAA's jurisdiction... what is the problem exactly?
One presumes they still need to know the location of those flights to deal with them descending into the range of altitudes used by commercial aircraft.
No commercial aircraft operate at such altitudes. No, seriously: you run out of air for air-breathing engines above FL600 (the SR-71 flew at FL800 very fast indeed partly because it needed to go like a bat out of hell to keep enough airflow through its engines: and because it was able to go that fast due to there not being much air up there to produce drag), and the turbofans used on commercial airliners rapidly run out of wheeze above FL400.
The only civil aircraft that ever flew above FL500 were Concorde and the Tu-144, neither of which are in service. But they didn't fly at supersonic speed and high altitude in crowded airspace -- simply because getting an SST up to altitude and speed takes several minutes, a couple of hundred miles, and a prodigious amount of fuel. To say nothing of the sonic boom issue, which basically limited supercruise to over-ocean flight.
While there's been a lot of hot air about supersonic bizjets over the past two decades, so far nothing's escaped from the CAD package much less gone into flight testing.
So what you're asking for is for an FAA system to be retrofitted to handle exotic military requirements, future space shuttles, and a class of commercial aircraft that would not operate in that flight regime within a couple of hundred miles of any airport.