Some of the reasons for using a Triac over MOSFETs are: lower cost for equivalent voltage and current ratings, requirement of only a single device, and, quite frankly, tradition. MOSFETs have historically not been very practical for controlling AC loads given the higher voltages involved.
For those used to working with MOSFETs as DC switches, rectification of the AC power seems like a logical approach for some loads. But in reality, rectification adds additional components, lower efficiency, and additional losses (heat dissipation).
However, rectification is not actually required in order to use MOSFETs. AC power can be directly controlled with a pair of back-to-back MOSFETs, in series, sharing a common source terminal:
simulate this circuit – Schematic created using CircuitLab
The lower, DC part of the circuit above can easily be controlled by an opto-isolator.
Only two MOSFETs are required, and assuming you have galvanic isolation worked out, gate control is very simple, as the MOSFETs share a common source terminal and are both switched on together regardless of the phase of the AC cycle. Phase angle or zero-crossing detection is not necessary either, although you may want to do it for purposes of reducing device stresses and electrical noise during switching.
Unlike Triacs, MOSFETs can be easily paralleled for lower resistance, additional current handling, and lower heat dissipation.
It turns out that modern MOSFETs can also be significantly more efficient than Triacs:
A typical 650 V Triac has a relatively constant forward drop of 1.55 V. This equates to 15.5 W of heat dissipation under a 10 A load, requiring a substantial heat sink (or possibly active cooling). Triacs are not easily paralleled for better performance.
A nice 650 V MOSFET, such as ON Semiconductor's NTH027N65S3F, has a typical on-state resistance of 23 mΩ. Since two are required in series, that's 46 mΩ total, resulting in 4.3 W of heat dissipation under a 10 A load; less than 1/3 of the Triac. Passive cooling with a relatively small heatsink is much more practical.
Because of the relatively constant voltage drop, heat dissipation in a Triac tracks mostly linearly with conducted current: P = I * V. In contrast, heat dissipation in a MOSFET follows a mostly quadratic relationship with conducted current, due to a relatively constant on-state resistance: P = I^2 * R. In a low-resistance MOSFET (e.g. 46 mΩ as mentioned above), the heat dissipation curve is well below the straight line of a comparably rated Triac, up to nearly 30 A. Above these currents, a Triac would dissipate less heat, unless you use lower resistance MOSFETs or parallel multiple devices to a achieve a lower resistance (something you can't really do with Triacs!).
The downside is that the cost of using MOSFETs is about 4x higher than the Triac. However, control is easier and the circuit design is quite simple.
With any solid-state AC solution, I would protect the device with MOVs and definitely incorporate a separate fuse or breaker for safety purposes.