Understanding how a motor "works" is the first step to understanding how to control one!
When at rest (ie not spinning) a motor is just an inductor. It has a small DC resistance, the larger (physically or powerfully) the motor, the smaller this DC resistance will be. Typically, you'd be looking at a few ohms for a small motor, and just several milliohms for a big one.
So, if you apply a fixed dc voltage to that motor when stationary, V= IR, so you get a large current flowing. However, due to the inductance of the motor (it is after all, designed to make a large magnetic field in the air gap)that current doesn't start flowing immediately, but takes time to build (how long depends on the inductance)
The important point however is that as a motor starts to turn, it generates a voltage in the opposite direction that the supply. This "back EMF" fights against the supply voltage, and hence acts to reduce current flow. The important point is that this back EMF is just proportional to the speed of the motor and nothing else (at a first order).
Imagine a motor that has a back emf characteristic of 1 volt per 1000rpm. If you were to connect it to a 5v DC supply, it would start spinning until just before the back emf equaled the supply voltage (in this case, just below 5000rpm). It cannot ever quite reach 5000rpm because if it did, the back emf would be exactly the same as the supply voltage, and so there would be no forward voltage left to drive current through the motor (and hence make torque).
But, lock that motor solid, and the "stall current" would just be set by the supply voltage and the motors DC resistance, because when it's stattionary there is no back emf.
So how does this all apply? Well, if you have a system where the motor could be completely stalled, and your "controller" just applied 5v say, then yes, you need to be able to supply the full stall current. But if your system uses some other technique to apply a proportion of the supply voltage (PWM for example) and can vary how much voltage it does apply (and even better measure the current that is created) then the stall current value is much less critical.
You can "soft start" the motor by only applying a small percentage of the supply voltage whilst the motor is stationary, and hence limit the current drawn.
Most motor controllers will have in "inner" current control loop (that drives the output voltage (via pwm) until the current reaches the target value) and an "outer" speed control loop that demands the current necessary to get to the speed target. In this way, the inner loop prevents overcurrents and controls motor torque, and the outer loop prevents overspeeds and controls motor speed.