That's right,you should use MOSFET-based rectifier.This is useful however only if (Ron)X(I) is less than 0.5V,otherwise Shottky barrier diodes are more appropriate.
Example: BUZ11 has 0.04ohms resistance in ON state.If the amplitude of the current is greater than 10A,you should either use two MOSFETs in parallel or resort to shottky diodes.
When the curent is 200A for instance,MOSFET is not an option.
Consider the complexity of syncronous rectifiers-at least some more windings of the power transwormer.