I have used equalizers for 50 years. I have three in my rig right now. I don't have time to go into it now, as I'm leaving for the Twin Cities. Later.
So I have arrived back in the Twin Cities.
Yes, analog equalizers come in 2 favors. The first is the band octave equalizer. In fact often split up into fractions if an octave into 30 bands or more. Common, used to be the 10 and 12 band equalizers. The center frequency of the band can not be changed.
The more complex parametric equalizer allows he center frequency of the bands to be adjusted, and their width and Q.
Now as others have stated they have a high propensity for misuse, with awful results. Basically if the faders are pushed to extremes, or worse one band has a lot of cut and an adjacent one gain then severe ringing starts to occur.
In the analog age of the LP and tape machines properly used they served a purpose. They don't have much value in the reproduction of properly recorded and produced digital music.
So I will tell you what I have used them for and go back in time a little.
The LP was particularly prone, and still is, to rising distortion above 7 KHz and sometimes starting at 5 KHz. In addition some earlier turntables had rumble and the cutting lathes also.
In the fifties and sixties, preamps integrated amps and receivers often had rumble filters.
The UK manufacturers, Quad founded and run by Peter Walker, and Leak run and founded by Harold J Leake, had ways of dealing with the HF problem.
All Peter Walkers preamps had a slope control. This consisted of two controls. One control set the turnover frequency at either 10 K Hz, 7 KHz, or 5 KHz. The other control adjusted the slope after the turnover frequency. It was absolutely brilliant and improved LP enjoyment enormously. Leake had their Varislope, but Peter Walker's was he best. It could also be used to tame tape hiss.
So this gave the push for equalizers that could be inserted in the tape monitor loop.
Now some problems are so severe that more than the slope control is required, but not often.
All my turntables are connected to a Quad preamp, and I would never be without one to enjoy my legacy LP collection.
For more severe problems in the early 70s I bought a Spectro Acoustics 2 10R equalizer. This was a highly regarded unit and they still get snapped up on eBay at a good price. Swerd, you might be interested to know that none of the sliders have ever become noisy. It took Far Eastern manufacture to create that problem.
Now I use that unit so I can switch it in after my switch bus to handle the odd particularly difficult LP or prerecorded vintage reel to reel or cassette tape. I do not have many of the later.
Now I also have a Mackie equalizer than can be switched in ahead of the DAC to my DAW, I use for archiving. For a quick check it is easier than the equalizer in Wavelab. Once I know where to head, after making a Wav. file then I can Eq the whole file at once in a fraction of a second. I can even do a whole batch of Wav, files with the digital equalizer in WaveLab.
The other equalizer is to bring up the last octave a little on my vintage Brenell Mark 6 reel to reel tape recorder. It seems only Herr Willi Studer could design and make tape heads that would extend flat to 20 KHz. All others roll the bass off from a little to a lot. The Brenell has Bogen heads which can benefit from a little lift below 30 Hz. The Far Eastern tape heads are by far the worst in this regard. Their machines were also thrown together and hard to service. So I avoided them.
What an equalizer can not do is what you want, and remove individual instruments. That can only be done of a multitrack master..