Why fast inner current loop and slow outer loop of DC-DC converter
In any control system with an integrated function, such as a pulsed voltage thru an inductor and resulting current integrated to an output voltage makes is very sensitive to overshoot and settling time with say 25% step loads over the whole range of rated current. The result is a change in loop gain which makes the PID servo voltage with a single feedback voltage less than optimal.
When load current changes quickly you want to respond quickly with supply current so you have a 1st order or proportional feedback (P of PID). Similarly for regulating voltage with slower changing voltage one uses voltage feedback. Ideally, you always want  1st order feedback on disturbances (load current) and 1st order feedback on the output variable (voltage) giving a dual loop for better results with some integral and derivative gain to complete the optimization for overshoot and settling time.
The same is true for position servo's in HDD's, and all sorts of control systems.  In some cases, there may be many variables and one feedback loop for each output variable only if the stability of each variable is important, such as acceleration, velocity and position.  It is also true for PLL's with frequency being the integral of the phase comparator.
The block diagram will look something like below for a boost converter.

The time constants of each loop may be much faster than you suggested depending on the driving rate and energy storage time constants with the output Cap, C*ESR=Tau being one of them to handle very short term transients, such that the bandwidth of that servo must be faster than the cap storage bandwidth \$f_{-3dB}=0.35/(ESR*C)\$ in order to regulate step loads.