Are capacitors necessary for an ESC (Electronic Speed Controller) design?

Yes, generally speaking. Bus capacitance is required to supply the ripple current caused by the PWM switching. The ripple current is a function of:
* (increases with) bus voltage,

* (decreases with) stator inductance,

* (decreases with) switching frequency.

The amount of capacitance required is dependent on the ripple current each capacitor is capable of sourcing without reducing its lifetime (part of the manufacturer's specifications), and the ripple current your power supply can handle without exceeding your maximum desired ripple voltage. For example, if you have a dedicated power supply close to your drive that has its own large capacitance, you may not need as much on-board capacitance as a system which must share a power supply with other loads.

A readable paper on sizing capacitor banks can be found at:

http://www.eci-capacitors.com/pdf/whitepapers/IEMDC_2009_11310_Final_Rev_4.pdf