Great observations Don01. The different diameter pulleys do have different effective ratios. If both pulleys are the same size it would be 1:1. If the motor pulley is half the diameter of the load it is 2:1 (ie 2 revs of the motor for 1 rev of the load). Like a gearbox, power in = power out (-losses) so the change in speed results in torque multiplication. There will be a lot more torque (grunt) available to the load at lower speeds and people do use those speeds for that purpose. On a direct drive (no pulleys), providing the same power at half speed (ie 2:1 ratio example) will require a %200 (torque) overload on the original motor. Please read on, it gets worse...
Even if you do not overload the motor (ie. never exceed nameplate current at any speed), you will probably still burn it up. The killer here is cooling, or lack of it. For a standard TEFC motor, the speed range over which you can operate at full torque may vary from less than 2:1 to as much as 4:1 (don't confuse with gear ratios/torque multiplication). This means that a 1800 rpm motor may be able to run full torque at 900rpm (a.k.a. 2:1 constant torque speed range) or even down to 450 rpm (4:1 CT speed range) before the lack of cooling causes it to exceed the insulation temperature rating (ie. burn up). The variables here are fan design, type of enclosure, and insulation temperature rating. Normally you need a motor with a separate blower (ie independent of shaft speed) to achieve speed ranges greater than 4:1. My guess is that a machine tool (woodworking, etc) motor has very little constant torque speed range (it certainly wasn't designed for one).
I don't know what type of pulley ratios you have, but I would bet that there is some serious speed reduction/torque multiplication going on. If so, the pulley system you have is the best way to do what you want. It would be quite costly and electrically ineffecient to size a motor for direct drive (ie many times bigger than what you have now) and then add the requirement for a wide constant torque speed range.
I know you were hoping for a different answer, but I hope this helps.