I told myself I wouldn't get into the convo about "burn in" or what causes it... I guess I'll jump in. I do have some relevance to the TWS600 though, skip to the last paragraph.
As you use a pair of tips more, they will change in shape and the silicone will become more pliable. This is strongly evident in the Etymotic tri-flange tips I use with my HF2 and ER3 as they become more and more ovular as they are used and eventually won't hold onto the IEM as well (either the seal becomes much stronger, the silicone gripping the IEM stretches, or both). Most tips I've used get softer as I use them more as well. Ear pads (for both on and over ear) will compress with time as well which changes the driver's distance and angle to one's ears. That and the foam will conform to your head better. Again, ear pads tended have different pliability as they got older. The part that creates a seal with your head/ear physically changes, and pretty drastically I might add.
There's also the hypothesis that our brain probably does adjust to the sound when you listen to the headphones more. However, just as quickly as it can get used to the signature, it can lose this if you were to not use the headphones for a while (say months or years). Though I've never seen one person claim their headphones sounded like they were fresh out of the box after not using them for a while. Especially with headphones that didn't have the best signature out of the box.
Then we get to the drivers which with dynamic drivers which move, flex, bend, etc. as they are used. You repeatedly do this and overtime its properties (mainly resistance to movement) will change. Mainly they may exhibit more give/flex (kind of like the silicone tips do).
Personally, I have no clue what causes people to perceive the sound of the headphone changing with time. It's quite a well documented effect. Though it has many, many variables in play, most of which are confounding as well. I've made my opinions about the brain getting used to the sound above, it probably does have an impact, but not as large of one as it you make it seem. Every time I've gotten new tips for my Etymotic headphones, the sound signature has changed slightly, so I feel like that's part of the equation at least. Though they are the only tip I have that tend to wear down to failure (no longer able to hold a seal). Despite this, to me anyways, they still don't sound like they're like new when I swap the tips (though I might be wrong with this since it is indeed subjective). I personally don't know what causes the perception of break in, but I would wager that there is more than one thing at play.
I also do remember an instance where I exchanged my ADDIEMs for a new pair, they let me keep the old tips (which I continued to use until the stem not longer held on to the IEM anymore). The new ones sounded completely different (like the previous ones I had when they were new) than the old ones but after about a week of use sounded like the old ones again. Granted all of this is indeed anecdotal which is why I stand by my statement that I don't know what causes it, but I hypothesize that there are multiple parts to the system and they all have some impact.
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Quick tip to try to help with the harshness of the signature is to actually test different tips and insertion depths. Try to find a tip that will both improve (or not change) the bass response and reduce the 4k spike (preferably both, but I'd personally preference the reduction of the 4k spike over the bass, but only to an extent). Additionally, for me anyways, a shallow insertion (that maintains a seal) instead of a deep insertion (that also maintains a seal) seemed to help with the 4k spike as well without aggravating bass response much. This had a larger effect than the tip selection (though tip selection did help as well). YMMV though as the tip selection and insertion depth is dependent on your physical ear's anatomy. Granted you'll never get rid of the 4k spike, but playing with different insertion depths can help at least make it more tolerable, maybe even become tolerable. I mainly talk about insertion depth because the harshness I hear sounds almost as if it were a bad resonance at the graphed 4k region (the last headphone I had that was nearly this bad was the first gen MEE A151 that I had). Adjusting the distance between your ear drum and the driver may help mitigate this.
I kind of feel the same way actually. I do wish these had a bit more bass presence on them, maybe a little more body. In many ways I reminds me of how I remember the RE0's* bass response, runs in the family I guess.
*anyone remember these? They were my second or third "good" IEM I got when I first started this hobby and hold a place in my heart