Yeah, back then computers wouldn't have been practical for ad-hoc calculations, what with being huge, expensive, and you needed to program them, and probably still with punch cards. And even after pocket calculators started, I'm fairly sure that at first they couldn't do advanced operations like logarithms and trigonometric functions. IIRC the first that could do that was a Hewlett Packard in 1972, but it was very expensive. It took until the second half of the 1970s for slide rules to become truly obsolete.

Maybe Starfleet navigators and engineers have to learn how to use slide rules to be able to calculate their course and warp formulas or such even while their electronics have crapped out on them. I mean, considering how often they seem to have trouble with the beaming and the communicators, maybe it's best that they have a low tech fallback...