Disadvantages of MOSFET over Triac for line voltage control of AC/DC devices
One of the issues is that Rds(on) increases rapidly with breakdown voltage rating for MOSFETs (for a given die size) and it does not for triacs, SCRs or IGBTs, so high voltage high current MOSFETs tend to be expensive and/or require expensive protection against transients. 

When you rectify you're also adding two diode drops' worth of losses. The triac avoids that. 

Nothing is really perfect, but in the 10+A/240VAC range triacs (especially in the form of SSRs) and mechanical relays or contactors stand out. In the first case you have heatsinks to provide (which may cost more than the SSRs) in the second case you have lifetime to worry about. Solid state switches tend to fail 'on' and can easily be destroyed by a heater failure, even with expensive fuses, unless grossly overrated (and thus more expensive). It's fairly easy to protect a 40A triac with a &lt; 5A load, but not so easy at higher currents. 

Mechanical contactors can withstand a bit of abuse (transients, surges) but have a defined life. And they click, which may or may not be an issue. It would be nice if we could buy a solid-state device which could withstand a 2000V surge, a 500A momentary short AND had almost no losses, but they don't exist, at least not at an affordable price because acres and acres of silicon would be needed. 

We used to use mercury displacement contactors because of the very long life, quiet and cool operation and only occasional explosions, but they are verboten these days in many situations.