An airliner's service ceiling is the altitude at which its rate of climb drops to less than 100 fpm. Most commercial airliners can't climb above 40000-45000 on a standard day. If temperatures are above standard, less than that. Corporate aircraft can go higher, just above 50000, so they get to avoid pretty much all the traffic because everybody else is below 40. The Global Express uses low bypass fans and very large wings to do this.
To go toward 60k you need super efficient engines and glider like wings. P&W developed the U2's engine with virtually no blade tip clearance to be able to operate at 70000ft.
Then you have coffin corner, the spread between critical Mach# and stall. It gets pretty small at 60000 ft. In the U2 at 70000 ft the spread between Mcrit and stall is very small, and between Mcrit and the back side of the power curve is just a few knots and they cruise in a tiny speed window, autopilot on in speed mode at all times. Bit too slow and down you go, bit too fast and mach buffet starts.
At an airliner's service ceiling, you have very little reserve thrust margin, and you may be operating just above min drag speed, not so far from the back side of the power curve in cruise. If you are at service ceiling and some speed bleeds off because say you hit some down moving mountain wave and the autopilot pitched up to compensate, and you aren't paying close attention, you may have no choice to descend right away as speed decays with no way to stop the decay without resorting to gravity.
Stalls at this altitude take many 1000s of feet to recover from. In the thin air, a mass has to accelerate over twice the distance through space for the same indicated airspeed increase as down low. If you get stick shaker at that altitude, you have to push over really aggressively for the recovery, not just lower the nose a bit. After a fatal Pinnacle Airlines CRJ200 stall incident that started at 41000, airlines started to focus more on training for high altitude stall recovery.
The high altitude world is a dangerous place, even at altitudes in the 30s.