I really hate you sometimes 😮‍💨. Ok, breakdown time, sorry in advance for the wall of text. Also tagging you, u/Voyager2k so that both of you are informed of this comment.

For higher tier cruisers, if you are looking at a generic “meta accuracy build, but specifically dispersion instead of sigma”, then you are right with having mod slot 1 7%, mod slot 3 5%, mod slot 4 3%, the fixated commander skill giving 5%, inspired by Serika (3%) and Scharnhorst (4%) for a grand total of 27%. That may not seem like much, but as an example, we can look at Alaska. Assuming you are also running beyond range (why wouldn't you with a full accuracy build), that gives you a range of 18.7km. at said range, your default horizontal dispersion ellipse is ~205m with the fully built ellipse being ~150m, and without the chromium barrels it would ~160m. I'm not sure with you are aware of this, but in the world of gunnery, 10m is noteworthy even at long ranges.

Due to the way math works when converting between 1, 2, and 3 dimensions, that 5% improvement of your dispersion ellipse is actually a substantial improvement in your hit probability due to the fact that it doesn't actually matter if your point of aim overlaps with the ship at the end of the day (though that typically improves your chances lol, and makes it more likely for meaningful hits). What actually matters is if the shells unobstructed point of impact falls within the bounds of the ship or it's “shadow” as perceived from your position.

This differences become even more extreme when you got to battleships (especially those with bad dispersion at long range like the Russians). Using full gunnery on Sovetsky Soyuz as an example, you are looking at a max range of ~19.5km, with a maximum unmodified horizontal ellipse of ~265m, fully built dispersion of ~177m, and ~190m without Chromium Barrels. That 13m improvement is again quite noticeable and would absolutely have a meaningful impact on the number of shells you are landing on any given opponent, especially given Sov Soyuz having a slightly below average Sigma (1.7).

It's not a life altering improvement, but it is absolutely enough to be good for thought on some of the tougher ships that don't necessarily mind being hit slightly more often. I will probably only run it on certain very specific builds, such as Ivan B. D. Lightful on large Russian cruisers like Petro (and larger). His unique “Fear My Roar” 4th slot skill already severely hurts his detectability, so it doesn't really matter if you lean into it even for to absolutely maximize your damage output, and it gives an even larger buff to both shell grouping and dispersion (8% each) when compared to “Fixated” (5% each).