That seems the same problem of "why train track spacing is like it is" and the answer is "nothing actually technical".

1,2,5 series woud've been much more useful considering how often in electronics you need integer ratio of some 2 values

Well, the 1, 2.2, 4.7 E3 sequence that is embedded in the E12 sequence is plenty close enough for almost all applications. The successive ratios are noticeably more consistent than for the 1,2,5,10 sequence (2.2, 2.14, 2.13 versus 2, 2.5, 2)

They were probably chosen because the decision was made in concert with manufacturers who wanted to be able to continue to buy/build with the values they had before.

I’m surprised so many here are taking issue with the answer on the page. It’s a reasonable answer reflecting a pragmatic process. Just don’t rug-pull our existing components and give us more variation.

And don’t give me “you can get odd numbers with two resistors” — at the time this was done, these things were not cheap, they were not small, and doubling your component count and increasing your product size because of a new government standard would not have gone over well.

You can ask that question, too - but it's irrelevant to the question why the E12 series was changed in this way.

The original question was why E12 10^(n/12) was misrounded. The wikipedia page only explains why the E system was E12 inatead of E10.