As an ex-20 year carpet cleaner, I know that properly cleaned carpet will be dry withing 4-8 hours.
Unfortunately, to get really dirty carpet really clean and then really dry in this time period requires something like $40k in cleaning equipment and in certain weather conditions may require additional drying equipment. Not to mention that you have to know how to use the equipment properly.
Not exactly a do it yourself situation.
How dry is "dry"? I was refering to the carpet/pad being at a state where it was more moist than the surrounding air, not squishy wet. You're right, that goes away quickly if your vac is powerful enough to pull it out. You probably used a truck, right?