I don't think you should mix flat at all. I am looking for those bumps and troughs during different sections, but for massive hard hitting chorus's I do think it's good to get a very dense flat/limited/wide frequency response (wall of sound) for maximum impact when those type of songs call for it. This is obviously not the case for every song though. I wouldn't be surprised if the Abba songs looked pretty similar during dense sections if they exist. I would still learn a ton if I used a spectrum analyzer on those Abba songs, I'll bet no key element is jumping out though. and although there are gaps in the frequency spectrum you could probably still draw a line across the peaks and see nothing jump out way above it.
I'm never tempted to fill in holes in the mix if I see one.
But the very common problem in mixing is if you have 1 bright element, then you will have a tendency to mix everything else a little brighter and get a harsh mix, or if you have an out of control kick, you'll might balance to that, not as common because as MrRoush said above, our ears get so used to things being bright, our ears literally EQ that stuff out by themselves after a while, you can't tell me that you have never mixed something too bright! Just based on that fact, how can a spectrum analyzer be such a terrible thing? And no matter how often I successfully mix translateable mixes, I still do fall into that trap. I'm Human, even pros do this. It's a regular discussion I see and is what makes mixing so challenging. Especially for those that do long hours on it, instead of little and often.
A lot of the older music from the Kerrang era can look pretty wild at 10k etc. But.... this is why a lot of those songs can sound like ass on smaller speakers, all you can hear is spshh spshhh spshh from the crash's. But they do have an exciting element to them when listening on speakers with broader response.
The analyzer just helps me pick out glaring faults that I may otherwise miss with the onset of ear fatigue. The analyzer is just a metering tool, and as metering tools go, they get you in the ballpark. I can mix a song that looks flat using a spectrum analyzer but sound muddy/indistinct as hell, so ears are needed for the left to right frequency balance aswel as amplitude because in this regard an anaylzer isn't very useful at all.
To be honest, for an aspiring mixing engineer, the first plugin I would recommend would be Metric A/B, which is an all in 1 referencing tool, it details everything you need to know if you are serious about matching your reference as closely as possible, lufs, stereo imaging, spectral balance, with an automatic level matching function so you can flick between your mix and several other loaded in references in real time. I don't think I would be doing him a disservice at all. Referencing is important, and referencing with amazing metering tools can only help IMO!
It's almost at the point of this discussion that if the advice is to just (use your ears) then why bother even using references at all. It's ridiculous.
edit: I wouldn't recomment to anybody else other than a beginner, pro's don't need references, metering tools etc. but a lot of us do not have the luxury of mixing 8-16hours per day for 30years.