Well I have 20 different headphones haha. IMO there are parts of your question that are highly philosophical/personal and parts that are a bit more objective.

On your part about EQ. Two things. First, I know there is a group of folks in this thread that may say otherwise, but EQ is not the end all be all in sound presentation. For example, no amount of EQ is going to make my Sennheiser HD660S2 have the soundstage of the HD800S - and there are listening scenarios in which sound stage makes a big difference (for example, high quality live rock concert recordings and classical recordings) - and maybe one wants that big 800S stage when listening to stuff like that but not so much when listening to other genres. Gaming is another, just off the top. There are other things about a headphone that may not be adjustable with EQ as well such as timbre brought about by the material used in the diaphragm, its ability to layer/position pieces of the mix well, etc.

Second, EQ is not necessarily an easy thing to get into. There are different “levels” of EQ if you will, and like many things in this hobby, the “best” can be constraining. For example, I am fully in the Apple ecosystem and have multiple devices that I use both at home and on the go (I have to travel a lot for work, and sometimes just don’t want to be confined to my office with my desktop gear when I’m listening at home). If I have to EQ a pair of headphones (some of which I do), I have to consider what DAC or software I’m going to use to EQ. There’s a big difference between hitting a bass boost or something like that and doing a detailed EQ profile. While you may view having 5 pairs of headphones as weird, I would view spending a grand or more on a pair of expertly tuned headphones, then using a simple “rock” EQ on iOS to be even more weird lol.

This leads to my personal reasons for having the collection. Reason number one is listening flexibility. For example, when I’m in the mood to listen to some hip-hop and just want to bang out and jam, I may break out the LCD-X and EQ the heck out of it, boosting that legendary bass and lifting up the overly dark midrange. It’s for sure way too bass heavy, and using EQ with my Chord Mojo 2 is fairly decent but nowhere as good as more detailed options, so I now I’m also giving up tonal accuracy in other areas to do a pleasant EQ for this listening scenario. The LCD-X does that kind of “fun” tune extremely well (because it takes EQ with almost no distortion, as you mentioned).

If I then want to listen to Adele, I could put the LCD-X back to stock (probably not with its veiled midrange) or EQ it for Adele. OR, I could break out my Focal Utopia, which has the highest vocal resolution and most natural vocal presentation I’ve ever heard, and also has a soundstage that puts vocals front and center (much less wide than the LCD-X). Many of those things can’t be EQ’d. It’s also a dynamic driver and can’t reach the bass levels of the LCD-X, so I could not do the hip-hop scenario with the Utopia.

Every headphone of the 20 I own brings something unique to the presentation, and that uniqueness may work well for a range of listening scenarios - though there will also be tradeoffs. The practical part of the collection is learning the tradeoffs I’m willing to make for which listening scenarios, acquiring stuff that requires me to make less tradeoffs overall and acquiring stuff that brings new special talents to the table (hello Meze Empyrean II).

The not practical side is that this is just my chosen “thing.” I believe everyone should have at least one thing he/she/they sort of geek out on, and for me, it’s headphones. I would likely never tell someone that 20 pairs of headphones are a “need” - just like 100 pairs of shoes aren’t either. But if you have the passion and the funds - why not? There are worse addictions obsessions…