...For all we know, the mighty Excelsior
was chosen as the final testbed because ships smaller than that could not have accommodated the bulky, primitive gear needed for the transwarp experiment. Starfleet took a look at their current inventory and decided they could spare their latest big battleship for a few months or years of experimentation, now that she had proven herself in conventional ways already.
If transwarp showed promise on small scale but needed a really bulky testbed for final verification, then it would not be completely unreasonable that it might have flopped. Promise until a certain point, then revelation of unexpected troubles at high power levels unattainable by lesser testbeds, then realization that the basic theory was all wrong and could never be used to build working machinery.
But it's equally possible that transwarp was proven in practice before being installed aboard NX-2000; the big-ship-for-clumsy-equipment aspect could still drive Starfleet's decision on which existing starship type to first equip with the wonderful new drive - but a more conventional rationale on the lines of "the best for the best" would also apply, and Starfleet's pride would get the drive first, while lesser vessels would have to wait.
In any case, NCC-2000 in her operational guise has this fancy big cavity in the aft ventral secondary hull. We never see this part of NX-2000 on screen... Perhaps transwarp machinery was originally fitted in there, and its removal left a hole that Starfleet to its delight found very useful for other things (blue-glowing forcefields suggesting a shuttlebay on NCC-2000, various greeblies in there on later ships).