To DatsRight: I wouldn't personally say that Ash ever fully matured. That never happened and it hardly will since it would require more deeper and sophisticated development of protagonists in anime like this.
You can strive to reach such kind of position and state, but there will be always left room for improvement. Making things better than they are searching for ways to go beyond your limits reaching new level. Because just like we human beings can never call ourselves fully matured individuals having flaws, imperfections and moments of childish outbursts going on surface, same applies to fictional characters always having ways into his advantage etc.to better themselves.
In Ash case alone during AG, as character he still tended to naively enter in battles without thinking and developing proper strategy, having problems in pulling out of his pokemon full strength, lacking knowledge and experience to overcome basic flaws certain type may have and turn it
Even in current Kalos series issues with Greninja, his overconfidence at times which may backfire sooner or later and rash moments of jumping in danger without thinking(like incident in almost dying in volcano) shows he still has room to learn.
There are also more finer and arguably deeper themes in life his character may be exposed to. Like whole love and romance aspect, potential burden of being aura guardian descendant, deal with responsibility fear of letting everyone down as new champion on case of winning league. In being opposed by huge popularity and expectations. Question Ash desire to become pokemon master and what does this represent for him?
Explore on Ash connection to Ho-oh, introduce his father in story causing emotional turmoils inside his personality, etc. (which pokemon anime director until BF Masamitsu Hidaka stated as possibility in case writers wish to develop Ash on more profound level during interview on pokebeach during 2008).
So there's that as well.
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EDIT:
As far as topic before like I said before I do not want new pokemon girl, but either Serena staying feeling like she could be fleshed out more or one of previous heroines like Misty who has lot of unexplored things and mysteries left to be answered being great character imo coming back. Especially given how it passed forever we saw original girl playing role in any capacity.
Because constant introduction of new girls who go through most basic and simple character development due to never staying long enough to reach higher dimensions in how far you can go with your protagonist both mentally and physically is just paravane. Cheap trick in smoking out much bigger and deeply rooted issues pokemon series are suffering from through temporary excitement and hype new face cause among viewers. Making them ignore problems and why cast changes(including ever so wanted removal of Ash from some)leads nowhere. As long current formula and status quo remains intact.
With there existing potential, unfinished plots and ways to do so much more with previous pokemon girls we grew up with and started to appreciate.