Such a simple circuit won't work with a brushless motor (though I admit I have no idea how you're trying to achieve your goal with that circuit). But there are several reasons:
-You need to know the position of the rotor in real-time so you know when to pulse and whart part of the sequence you should be pulsing. THis requires a rotor position sensor, or more commonly a sensorless back EMF circuit to detect the rotor position.
-A single pulse width for a specific RPM only works if the load is known and constant. Heavier loads require longer pulse widths (or more speciically duty cycles) for the same RPM. If this weren't the case, you'd be able to sprint with a heavy backpack just as easily as with no backpack.
-If using a sensorless back EMF circuit, a special startup algorithm is needed since the motor must be moving for back EMF to be produced to know where the rotor is. It needs to know the rotor position to properly send commutatation pulses to turn the motor, but it needs the motor to already be spinning so BEMF Is produced so it know the rotor position! Catch 22 if the motor is starting at zero speed a microcontroller).
-There are no simple high frequency switches that you can simply plug into a circuit. You have relays but they are SLOOOOWWW and wear out fast. Transistors are used but things are more complicated since the control voltage required is referenced to one of the primary terminals. Put another way, the control pin is the gate and the primary pin in question is the source. But the required control voltage itself is the voltage between the gate-source. Since the source pin is a primary pin, it will be at whatever voltage it is while the circuit operates- you can't control it really. And since your circuits will mostly be outputting signals referenced to ground it's going to be a problem since the control voltage at the gate is being referenced to the source (which may or may not be at ground). In bidirectional motor drives, this happens. So you have additional circuitry to deal with that- so called high-side gate drivers (versus the much simpler low-side gate drives). Knowing how to use a MOSFETs as a switch is critical.
-A quick glance at your circuit also only shows logic...no power components. To drive something like a motor you need the circuit to have the smarts to know what to do and the muscle to do it. Your circuit seems to lack any muscle and that is at least half the battle. Logic circuits in rare cases might satisfy the voltage requirements for the motor, but they never satisfy the current requirements. You can't hook something like a motor directly to a something like a flip-flop, logic gate IC, microcontroller and expect that ALL that power required by the motor is going to be passed from the battery to motor through that tiny little part.
Best to go for a BLDC driver IC, or make it from scratch using a microcontroller, gate drivers, rotor sensing circuitry, and the actual drive transistors. Just know you aren't saving money the DIY route.
Read through this, of particular importance is the commutation sequence. It will also give you an idea of what the circuit needs to look like an an abstract level (just replace IGBT transistors with MOSFET transistors for your application).
https://www.electro-tech-online.com/custompdfs/2010/08/00885a.pdf
https://www.electro-tech-online.com/custompdfs/2010/08/00857a.pdf
I suggest after reading up on this, go back to the drawing board and begin designing with the power stage first, then work your way backwards to the smarts that determine the proper commutation sequence. Investigating the power stage will introduce you to things like high-side gate drives, low-side gate drives, flyback diodes, power MOSFETs, H-bridges, and half-bridges (which is realy just half an H-bridge). The power stage of a BLDC driver consists of three half-bridges, one for each phase of the BLDC. This in turn is made up of power MOSFETs and flyback diodes. It is driven from the low power, control circuitry via the gate drivers. The control circuitry is usually a microcontroller.
Using a BLDC driver IC will tend integrate the control circuitry with the gate drivers, and for the lowest power motors will also integrate the power MOSFETs.