because the aircraft will only climb at one speed.
Well, actually, at absolute maximum altitude, the aircraft will not climb anymore. But in that situation you're flying at Vx which now equals Vy, with full power, and that's the only speed that will allow you to sustain that altitude. Any slower or any faster and you descend. For that reason the absolute maximum altitude is virtually impossible to reach and is of theoretical interest only.
The service ceiling of an aircraft is defined as the altitude where the aircraft is no longer able to sustain a certain minimum rate of climb. (Wikipedia suggests 100 ft/sec). At this service ceiling there's still some excess thrust so there's still a slight gap between Vx and Vy.
But you are right: The higher you go, the closer Vx and Vy will become. It's just that for various practical reasons you will never be able to actually fly at the point where Vx and Vy intersect. (Unless you have infinite fuel and infinite patience I guess.)
Ceiling (aeronautics) - Wikipedia, the free encyclopedia