What I’ve noticed, is that many newer cool white LEDs are 4000K instead of the 4100K of fluorescents. These colors are not significantly different but why are the LEDs 4000K instead of 4100K for most?

Also, why are cool white fluorescents 4100K and not 4000K? That’s another one to point out

It varies per market, EU market cool white is almost always 4000k.

Just market preferences and customs, i think.

Very good question!

Actually this goes back to the history of fluorescent lamp standardisation.  Many decades ago it was desired by many manufacturers to have FL lamps in discrete colour temperature steps eg 2700, 3000, 3500, 4000, 4500, 6500K.  Each manufacturer had their own unique phosphor composition to arrive at those values, which meant that the spectrum of one manufacturer’s lamp could be quite different than another even though their CCT’s were identical.  As such, their chromaticity appearances and colour rendering indices could also differ.  This was especially troublesome in large installations when replacing failed lamps of one brand by another : the differences were visually undesirable.

The lampmakers then began to standardise on the same phosphor recipes for each lamp colour, and the situation was greatly improved.  Later still, it was discovered that actually it was not efficient to target numerically precise colour temperatures.  For instance, by shifting from 4000K to 4100K it was possible to achieve a considerable cost saving in the raw phosphors, along with higher luminous efficacy, often a better colour rendering, and sometimes also better life.  There were large-scale collaborative efforts among the world’s principal lampmakers, co-ordinated via the standardising committees of the IEC and ANSI, to work out a set of optimal chromaticity points for FL lamps that would allow manufacturers to make better and lower cost lamps with improved interchangeability between brands.  These target chromaticities are specified in the relevant international standards and while they are not compulsory, it is highly recommended that manufacturers adhere to these.

When LEDs began to become popular for general lighting, both the ANSI and IEC performance standards encouraged nanufacturers to follow the same chromaticities and CCT’s as had been long established for fluorescent lamps.  This position was strongly supported by the traditional lampmakers and fixture manufacturers, so as to make the transition from traditional to LED lighting as seamless as possible.  However, the LED emitter manufacturers did not agree, for the very good reason that just like the performance and cost of FL lamps can be improved by targetting certain colour points, exactly the same is true for the available LED phosphors.  As such, led by the USA LED manufacturers which were formerly the leaders of that industry, ANSI standardised a different set of colour points.  Those have in the mean time been adopted almost worldwide.  The IEC LED performance standard continues to state that it is desirable to make LED products with same chromaticities as the old standardised F-series colour points, which is a bit silly because I think nobody actually does that any more.  Indeed, LED phosphors are also now developing at such terrific rate that even the ANSI LED colour points of the early 2000s are no longer always being followed.

As far as I remember, (at least for the EU market) the "4100K" standard flew out of the window with the introduction of triphosphors in the 80's, when the rated CCT became 4000K.

And I don't think it makes that much an effect, mainly compare to what the uneven room furniture/paint color scheme does - I had a pair of 4000K tubes in a kitchen, but the cabinet door were painted red. It looked like there were different tubes in the fixture, just what the reflected red from the cabinet did when reaching the fixture. And I was even able to even that out by using one tube of 3500K and the second of 4000K.
And needed to be said, in fact I was the only one who was bothered by it at all ( tell me something about the lighting bug  ) and it was not my kitchen, so I put back the originals, after all the lamps were not the culprit and it was not that bad, I just noticed it...

So I don't think 4100 vs 4000K would be that much of a problem, I would guess a bit of dust collected on/in the fixtures and the unevenness effects would be way worse even with tubes exactly the same...

Right now, I'm sitting in a room lit by a 4100K LED module (rated) which is (in fact) more like 4300K. No problem with that. It's simply cool white to my eyes.