Matt, you're close but a little bit off on those categories. In preparation for Conrail's creation, the USRA took all the predecessor railroads and identified them by segment. After research and input from various interested parties, they published the Preliminary System Plan. This gave a proposed list of what lines would be conveyed to Conrail and which would not.
After further input from shippers, railroads, and public entities, they published the Final System Plan. There were some changes from the PSP, other lines remained in the same status.
You imply that Conrail had to keep all the trackage for a while, which is incorrect. The fact is that many lines saw their last train ever on March 31st, or even a few days before. Other lines were continued in operation with Conrail as "Designated Operator", performing the service under subsidy while shippers either made arrangements to do without rail, or shortlines were created to take over. One problem from the shippers' points of view was that Conrail provided only necessary service, only as long as they were paid, and had no incentive to market or develop business on these lines.
The Avon-North Alexander segment was identified as USRA Line #1240. The FSP states:" This portion of the Attica Branch shall be offered for sale to the Chessie System....If this offer is not accepted, the portion of the line from MP 388.8 to 390.8 (Batavia) and 366.2 to 366.4 (Avon) will be transfered to Consolidated Rail Corp. The remainder of the line....is NOT designated for transfer to Consolidated Rail Corp....."
I would guess that 366.2 to 366.4 was the wye, and CR subsequently decided it was not worth maintaining and paying New York State's taxes on it.