Ultimately I guess one would look to the second derivative of velocity with respect unto acceleration, that is to say the rate of change in acceleration, but it seems that there could be a risk of being too good at fast stops.
The prewar Bluebirds were essentially PCC's with regard to propulsion and braking packages. Anybody dismissing track brakes for emergency braking is up against nearly 70 years of history with more than 5000 units field tested.
As I understand it, the distance between signal blocks must be such that emrgency braking would bring the train to a safe stop before it ran into ts leader. Accordingly, if emergency braking were improved, then I figure (am I wrong?) that more tph could be run.
Yes, you are wrong. The capacity limit is set by station stops. Service braking, not emergency braking rates, determine throughput at stations. This places the practical limit in the 40-42 tph range for reasonable values of braking, acceleration and dwell time. Service braking rates and acceleration rates of 4.0 mph/sec have been safely used on the PCC trolleys for almost 70 years.
I have noted that they used to operate 90 tph on the Brooklyn Bridge between Park Row and Sands St. They were not immune to the dwell time constraints. They had two tracks at each station in each direction. Trains alternated between the tracks - so that each track handled only 45 tph. However, nobody is proposing doubling the size of each station once CBTC is installed.
The question remaining or at least the one concerning me now, is of whether or not improving emergency braking would be cheaper than installation of a cbtc system, and what the respective increases in service per dollar spent on each (as well as how quickly these options could be implemented) option would be.
Almost anything is cheaper than NYCT's CBTC system. However, no CBTC system will increase capacity. It's determined by braking, acceleration and dwell time. CBTC doesn't change these one bit.