Too slow, and too expensive. And, as others pointed out, not environmentally friendly. Also, once they're dead, it's just making more mess to clean up. Also also, we miss the spectacle of the head being held up, and the potential to see the head blink or move the eyes just before death, and the noise would compete with the cheers of the crowd.

I vote for the cheap and reliable guillotine, which can be built by any handyman with a trip to a lumber yard. Line them up, read out their crimes and keep them moving. They just roll down a ramp into a mass grave, toss the head in after the body. Bury them, and build a solar farm on top.