I use a 12 month controlled release fertilizer and replace annually in spring. These products work much better when incorporated into the soil. Sitting on top the prills are dry much of the time so don't release any nutrient except for a brief window at watering. Under those conditions a 6 month osmocote may still be effective for a year or more. Instructions for use say best method is dibble holes and pour the osmocote in, second best is mix with soil at planting, last resort is to sprinkle on top of the soil.
No real need to remove used prills unless for looks. The coating gradually breaks down in the soil and eventually disappears.
Cacti and succulents don't need different nutrients they just need less because they are watered less so excess is not flushed away which can lead to toxic levels of nutrient or residual salts.
From a plant point of view there is no difference between nutrients from osmocote or from 20,20,20 or from fish emulsion. Controlled release fert is released every time there is soil moisture so is actually more efficient than twice monthly application of liquid feed where nutrient availability rises and falls as water leaches available nutrients out of the pot.