Is 15 sections too many for a journal article?
Yes, you improved it a lot with the 9-section outline, because:


It is much easier to communicate the tiered the structure of the paper to the reader, which makes readers and reviewers much happier.


It is easier for readers to scan through and understand the main outline of the paper, instead of having to figure out for themselves which points are more closely related.
It is easier for your to preview the shorter outline in words near the beginning, than if you're thinking of it as 15 sections.

It may slightly save you space, because subheadings likely take up less room than main headings.


Here are two additional potential revisions to further streamline:


Change point 5 into a subpoint under point 4. It's still about that simple algorithm. (As I just saw, lighthouse keeper also advises this.)
Shorten the title for 8.3. (Obviously, you're giving a generic version, but it could be done briefly by saying "Addressing Entropy Concern," replacing "Entropy" with a reference to whatever issue thoughtful reviewers may anticipate as a problem.)


Someone in your field may have better comments about whether the information you want to pack in here is all too much to effectively demonstrate in a 10-page paper. In particular, the simple, unscalable, mathematically interesting algorithm might not be as related to the rest, if you must cut something.