What about the Times Square shuttle, isn't that an IRT line with a letter?
True, but all shuttles in NYC are referred to by 'S', regardless of whether they're A or B Division.
Bringing things back a bit closer to topic, in a way many TOCs - and London Overground once upon a time - do already publicly differentiate their different services by a number (or less often a letter) designation - in the timetable leaflets.
For example, Southern have a different number for each of the pocket timetable for the Brighton Main Line (17), the West London Line (36), Oxted lines (29) etc.
Just shows the concept of lettering/numbering the Overground 'lines' isn't entirely crazy.
Just after electrification (so 60 years ago on 21 November), at LV, the new green units were distinguishable by their headcodes, eg 2T18 for Chingfords and 2M10 for Enfields, easily picked out when running for a train. Some distinguishing feature is needed at eg Stratford or Canonbury for the Overground nowadays. The platform displays are too small!
Similarly, SWR do have their old Southern Region route codes that are very occasionally used on Desiro dot-maxtrix displays, and are shown on the roller blinds on the 455s. I suppose NLL trains used to have a big 'B1' (and so on) on the front to tell you where they're going!
But I think for the public's sake any future line designation should stick to simple letters and numbers alone!