Variable speed is the ONLY way to go. I'm saying this after a couple yr of using a 3 speed pulley setup. A direct drive tends to run smoother. BUT - you asked about the why of slowing grinder speeds. I'll run max speed for profiling and rough bevel grinder with 36 to 60 grit belts. Then with 120 grit slow down some, then with 400 grit range I'll be down to the 1500 SFPM range. Then with anything in the 600 grit range I'll be down to <1,000 SFPM range.
Then when doing final grinds on scales I might be down to the 300 to 500 SFPM range. And when doing sharpening on 2X72 I'll run grinder in reverse and slow down to the 300 SFPM range and even 200 SFPM range for final grits and leather. Also, for working mammoth ivory and MOP you're really going to want slow speeds.
"IF" you have to purchase a motor, a 3 ph motor is about the price as a 1 ph motor, and a NEMA 1 enclosure VFD is less cost than 3 step pulley, jack shaft, and bearings. With filters installed over the air inlets the $70 Chinese VFD is going to last several years.
Ken H>
edit: I see Ed has already posted some of the speeds I mention. BTW, with a 4" drive wheel the rpm is pretty close to SFPM belt speed.