Back in the late '50s, one Col. Sidney H. Bingham, who had "put the Philadelphia subway back on its feet" (I dont' think it stayed on its feet very long) was brought to NY to try to save New York area rail commuter service. To quote a Trains magazine article of the time, "Col. Sidney H. Bingham retreats from the problem into pure fantasy." He proposed trains of all lines (including the subway) running everywhere on each others' lines, running from where people lived to wherever there were jobs, crossing from one railroad to another. Your map is somewhat remeniscent of that.
Bingham left unanswered the problems of incompatibility of signaling systems, differing electrification systems (and in some cases lack of electrification), differing clearance standards and car-length standards, differing safety devices, etc. And he also left unanswered the question of who would pay for all the infrastructure changes that would be needed, and what to do about differing union jurisdictions, and whether the system could pay for itself out of the fare box (not likely) and if not, how all the different states and municipalities would resolve how much each should contribute to the operation.