They're quite similar to slide rules in that respect. Learning how to use one gives you an intuitive grasp of the operations you might otherwise miss (or not see as clearly), but there are far better tools for doing the actual computation.
On a couple of tests, we actually had to analytically draw our smith charts on graph paper, then use it for then next problem.
Say you want 15 dB return loss at some frequency, well there are two impedances points for that. One with the impedance locus outside Z0, and another with the locus encompassing Z0. The latter has broader bandwidth, but that intuition is lost without a Smith or polar plot.
For actual measurements: there is much less ambiguity in a standard magnitude/phase response, since you actually can see the values of your independent variable (frequency).