Terry,
No, it is not impossible to output a 1(t) step frequency change, actually it is very easy to do so.
Imagine that the frequency is zero and you simply start outputting for example 1000 Hz frequency, then the change in the frequency is immediate which means that the acceleration time is zero.
Reaching that velocity in 0 time is possible below the stepper motor's start/stop frequency limit, that is an advantage of stepper motors that they can do that.
Ofcourse they will not accelerate up in zero time as that would be ofcourse impossible, but they can accelerate up so fast in that low frequency range that they can follow an immediate (zero time) change in the frequency without loosing steps, so it is close to infinite acceleration.
Again: S-curve profiling means that you can still use trapezoidal profile, you just setting the S parameter to zero and then there will be no S curve but the curve will be trapezoidal.
In addition we will have a frequency start/stop parameter under which the axis will accelerate with infinite acceleration and will deccelerate with infinite decceleration from that point down to zero velocity.
When accelerating to above that point then it will use the normal setup acceleration and the same when deccelerating and when reaching that frequency point.
So, in summary you can do trapezoidal profiling with the S-curve profiler and you can even do a 1(t) step frequency jump (or bang bang or whatever you calling it) below a setable frequency point.
But I think we already discussed the same months ago though...