Should I contact the EIC for additional information regarding his decision on my paper?

I just received the feedback from the Editor-In-Chief that my paper has been rejected for publication in this high-ranking journal.

There are several concerns raised by one of the reviewers. Therefore, it would not be possible to accept this paper for publication.

Based on the reviewers' comments, two of them seem to be in favor, as they raise no "substantial" concerns (they raise 5 and 4 points, respectively), i.e. their findings are mostly of a cosmetic nature (rephrase that, elaborate this, color the figures differently, correct a spelling mistake), and their recapitulation of the work is more precise than that of the third reviewer.

Now the third reviewer raises 6 points of concern. 4 of them are very valid remarks, however, they are not fundamental problems, at least, I don't perceive them as such, because they are easily amended (by at most 2 sentences each) and present no conceptual fallacies, i.e. as I see it, the particular parts are not clear to the reader and need additional explanations and more appropriate emphasis. The fifth concern addresses the structure of the paper, the reviewer proposes another ordering of the sections. The final point states the need for a discussion, which I indeed drafted, but chose not to include in the paper. It is not irrelevant, but it is not crucial for the problem, solution or background and could possibly distract the reader from the focus of the paper. In addition to space constrictions, this discussion was left out before submission.

Between submission and the decision, there was a change of the Editor-In-Chief at the journal. This might be the reason the review took longer than usual (10 instead of 6 weeks). Perhaps that could even influence the accepting policies...

After the first review, I'm used to getting rather harsh comments, either rejecting the paper or proposing another review cycle, it doesn't matter. The important part is usually that I get meaningful feedback about my paper and improve it. In this case, however, the reviewers' comments resemble something I would expect after the second or third review cycle, i.e. something that I can alleviate in a morning.

The problem is that I don't understand the reason for rejection. Even when I address all the reviewers' suggestions, I would still feel that nothing crucial has changed. Furthermore, when rejected, I can't submit the same paper to the same journal. I obviously intend to submit the paper to another journal. However, before doing so, I consider emailing the Editor-In-Chief and asking for more information regarding his decision. As things are now, the reviewers' comments state neither fundamental fallacies which imply that the paper is of low scientific value nor point how I could realistically improve on it. Is this a good idea?