It's very common to use thyristors in rectifiers in high power applications. They can scale up to many kilovolts and kiloamps and are used in HVDC links.

Linear and Intersil make COTS support chips. From a power supply design perspective it makes some interesting ideas possible, because you can turn a bridge rectifier on and off as fast as you want this way. So you can make a super low frequency switching power supply using the rectifier itself as the switch.

There are two obvious problems. First the voltage regulation is garbage because you're running 60 Hz instead of a typical switcher in the KHz region, so you'll be investing heavily in large filter capacitors or you'll have awful ripple on the output. Maybe it would make a good battery charger instead of using perfect regulated 5 volt USB power as typical? The other obvious problem is you can use four cheap diodes and one switching transistor on one heat sink, or four switching transistors on four heatsinks and probably a very small diode bridge to provide power to the chip to run the works (although maybe controllers have on chip rectifiers) And the cost at reasonable power levels of a switcher is a rounding error compared to its heatsink and the effort / labor of mounting it on a heatsink. So unless you'd doing some crazy electrochemical refining type stuff you'd probably not use a synch rectifier, just not economical. I bet hydrogen electrolyzer plants and aluminum and copper electrorefining plants DO use synch rectifiers.

If you have three-phase power, you can use a diode to each phase and dramatically reduce the voltage ripple, even without using filter capacitors.

Active rectifiers (ie. transistor based) are common in various high current applications. One quite weird example are line-interactive UPSes, which often use topology that allows same MOSFET bridge to be used as both rectifier when charging and frequency converter when discharging. Somewhat more representative application are various high current DC supplies, for example Vcore DC/DC converters on PC motherboards (12V DC -> <1V DC) almost invariably use active rectification.