I have read your posts very thoroughly, and it is the exact same post that I have already linked to above, and has already been addressed in very thorough detail.
What you are doing is comparing the templates to two templates that have custom html overrides. Our templates are only stylizing the default Joomla output. I have documented all of that in the post linked above.
The simple problem is that Joomla allows to determine several levels of subcategories to be shown but I can see only one level in all of your templates.
As far I thought this would be an "incline" Problem I tried to discuss it in the incline forum. After I was looking for another Shape5-Template which might perhaps solve that Problem, I testet nearly all your Joomla3 templates from the last years and found out that none of them was able to show what Joomla allows to determine in the categorylist-settings. Thats why the problem couldn't be any longer an incline problem but a more general one that must be discussed in a Joomla-Forum what means as far it is about Shape5-Templates exactly here.
At least I recognize that you did some more testing than your colleague to reproduce your self the problems I am talking about, that is after days without any serious answer at least a first step. And yes, it is not unimportant to know that shape5 does not use any overrides as beez3 and gavick music.free seems to use. (as you put it in your incline-forum-answer) It seemed to me in the first moment more probable to be exactly the other way round thinking beez3 would be a older less developed far more simple template than any of Shape5.
To summarize where we are right now:
a) For what ever reason: If Joomlasettings allows to chose how many subcategory-levels should be displayed in a categorylist menuitem than something is definitly wrong, when what ever one determine always just one level of subcategories is shown. It would be helpful to know that you consent, that this is definitly an unsolved problem.
b) If your templates are just giving what joomlas core code gives out, than it might perhaps be, that the reason is a joomlacode bug, what indicates your protostar-testing that shows exactly the same problem.
If so there seem to me still two things left:
- The first thing: one should do is to comunicate to the Joomla-comunity to let them test more if there is (as it seems) a joomla codebug so that they would adress and fix it
- The second thing: - what I still would appreciate from a good support - is to think about possible workarounds at least for the time until the bug is fixed in the Joomlacode.
I understand your general concerns about overrides. But if this would really be a joomla bug we simply need at least a temporary solution until the bug is fixed.
To ask more concrete, which line of the beez3 Override should I copy in my "default_children.php" to get the levels of subcategories displayed as beez3 (and Joomla 2.5 also has done it with your Vertex-template very nice) see here
Since not a single word of my answer depends on any incline-specific aspect i hope you understand, why I still think the problem is better discussed here.