There are a dozen spots in the steering that can wear and produce lash (slop) that some people would describe as a loose steering wheel.
You have to have someone turn the steering wheel back and forth as you move down all the linkages and look for the problem. When you see one part moving and the connected part moving less, you've found your worn part producing the lash. It is often a combination of several worn parts, like tie-rods or the steering box itself (it can be fixed a little by adjusting pre-load, a risky thing to do) and like mentioned the pins in the steering shaft itself.
It is rarely the splines on the top of the steering shaft and the steering wheel, trying to pull the cover on the steering wheel is unnecessary, just do as I describe, if it happens to be the extremely rare case, then you would see the shaft coming out of the steering column in the engine compartment is not moving at the same time the steering wheel is.