How important is to have faster refresh rate when it comes to spectrum analyzers ?
Are you referring to sweep time? That's basically a function of span and resolution bandwidth, both of which are user configurable.
As a practical (and somewhat oversimplified) matter: sweep time is important when you're measuring something that changes during the time it takes to make a sweep
If you're measuring the passband of a filter, etc. then it's mostly a function of your patience. Given that the "interesting" part of most filters is the upper and/or lower edges and attenuation in and out of the pass band, you don't need a terribly small RBW to get acceptable results measuring them*
(*unless you care about things like "ripple" in the passband, etc.)
The same could also be said for an amplifier that's being measured with a CW input, in which case the output signal is (or should be) constant and relatively narrow in spectrum.
The biggest reason to reduce RBW in both cases would be to lower the noise floor (DANL).
Yes, different spec ans will have different sweep times even given the same RBW and span, but for the tests you are describing I don't think the difference is terribly important.