One of the biggest discrepencies introduced with Fallout 4 is the whole "fusion cores power power armor and they run out" thing... In previous fallout games T-51 power armor had a practically unlimited power source as did later armors.

The only power armor described as functioning this way was the T-45...

Well... I have no definitive answers... all I can tell you is my head canon for why this is. It seems too me that in the game there technically is no T-51, or T-60, or X-1 power armor actually in the game, at least not a full set of any of these armors.

The Endoskeleton, the Frame, that is used to house all power armor plating is in actuality the frame for a T-45 power armor suit. These suits were probably infinitely more common as they were the first produced, and might have simply been cheaper to produce.

The frames for later power armor systems were probably far more expensive to produce because of their more advanced power systems, but the armor itself was probably easier to produce and thus the plating was shipped off to be used with older and/or cheaper frames.

the more expensive frames that were used and designed with better power sources would have been used closer too the war zones.

Furthermore, t51 power armor is said to be the pinnacle of power armor technologies, yet the stronger t-60 exists... perhaps the reason t-60 was never considered the pinnacle is because it never had an accompanying frame designed for it, or the frame for the model didnt get the chance to enter production and only the armor plating was designed for it.

X-1 is probably just the technical numerical designation for original enclave armor, god only knows how it got too the commonwealth but a lot can happen over the years.