Boost converter switch design
A boost converter follows the relationship \$ V_o = \frac{V_i}{1-D} \$ (ignoring non-ideal effects) when in continuous conduction mode (CCM). But with the diode as one of the switch, the converter would drop out of CCM at light load when the inductor current wants to reverse. If you replace the output diode with another active synchronous switch that would allow current to flow both ways, then the proportional duty cycle relationship can hold down to zero load because that would force the converter to stay in CCM. And not surprisingly, this is sometimes called forced CCM. (By the way, many boost converter does not operate in CCM at all in the first place.)

But the more important reason for feedback is probably this: Without feedback, the output voltage would depends directly on the input voltage (as seen in the equation) and the impedance of all the elements (the non-ideal effects of the switches, inductor, wiring) in between. That is usually not acceptable in most cases. For example, if the input voltage regulation is 5%, without feedback, the output regulation would always be worse than 5% and could be much worse for significant and changing load.