The children of the axes are the line(s) while xlabel is a property which holds the handle of the text label object. Until modified, it (the xlabel object) is empty (but does exist). If you'll look at
>> plot(rand(10,1)) % a plot; no visible x label yet
>> hL=get(gca,'xlabel'); % get the xlabel property
>> xlabel('x label')==hL % see if matches handle when write an x-label...
ans =
1
>>
Voila! the handle returned is the same as the property retrieved before there was anything in the object; iow, the axes created the xlabel but default is that its default value is the empty string so nothing shows up even though the object already is in existence.
Children, otoh, don't exist until placed on the axes...
Continuing on from the above--
>> close 1
>> gca
ans =
173.0067
>> get(gca,'children')
ans =
Empty matrix: 0-by-1
>> get(gca,'xlabel')
ans =
174.0067
>>
So, while the xlabel's parent holding object is the axes object, it is not one of the children properties which are the lines. This also demonstrates conclusively that the xlabel (and by extension y- and z- as well) exists with the axes object independent of xlabel the function.
It's a choice of organization when the handle-graphics objects were first constructed to segregate the fixed characteristic things associated with the axes such as the grid marks, x/y labels, etc., from the variable ones, namely the data line objects that could be from none to very many and give the fixed ones specific names for mnemonic purposes.
Also keeping them out the the children array means don't have to do extensive searching on the returned vector of children handles to find out "who's who in the zoo" when making changes to lines.
