Spectrum Analyzer: Resolution Bandwidth vs Acquisition Time
Filters delay signals - it's never instantaneous. Filters that have a very-tight pass-band produce a longer delay than filters that are wide-band. When you require a higher resolution, the filtering in the spectrum analyser becomes "tighter" and therefore produces a longer delay.

Looking at it another way - if you were weighing a bag of nails, you'd weigh it and get an answer. If you weighed the nails individually you'd get the same gross weight but it'll take longer. The benefit in weighing all the nails is that you get more detail - if that is what you are looking for.