So are you saying that TSFC increase with speed because of the increases 'Power Required' to produce the same amount of 'Thrust' ( since Power is the rate of doing word and more power would be required to overcome the same amount of drag at a higher speed ) , and/or the increase in 'Induced Momentum Drag' with speed ?
It's not so much a matter of overcoming drag.
Power is the rate of doing work or the rate of expending energy.
Power = Force x Speed
In the case of an aircraft in flight this becomes
Power = Thrust x TAS
So if we accelerate in flight, as our airspeed increases, if the engine thrust remains constant while the TAS increases, the power output must be increasing.
But power is also the rate of expending energy and we do not get anything for nothing. So to maintain constant thrust with increasing power we must increase the energy input rate. This means increasing the fuel flow.
So as we accelerate, we have an increasing fuel flow for a constant thrust. This means that the Thrust SFC is increasing.
Although this is shown in many text books, the same text books then quietly assume that SFC is constant at all airspeeds, when they deal with the subject of best jet endurance.
This is fairly typical of the way that we use (and become caught out by) simplifying assumptions.
bookworm
I hadn't really thought enough about it before, but this relationship between TAS and TSFC makes it even move obvious that optimum cruise altitude is a compromise.