Maybe I should revise the question a little... At what point does increased experience (with no further formal training) increase your limits in diving? It seems that there is a point with experience (plenty of it) that your limits likely begin to expand.
I think there are two different aspects with experience, rather like education.
Initially (when you first start diving). Experience is the part where you cement the existing knowledge (theory) and skills (practical) that you where taught on the course. i.e. you are now comfortable in the environment, (buoyancy, finning, ). You have experience of the types of diving you originally discussed - or like (have the opportunity) to do. This includes the basic skills (often forgotten), mask clearing, regulator retrieval, AAS.
(There are many experienced divers who may have no or extremely limited experience of a particular type of diving i.e. low visibility diving, drift diving, or diving in kelp forests. Because they have not had the opportunity or interest in this type of diving.)
At this level you are ready to progress - i.e. the next course. Your are mentally in a position to concentrate on the new tasks and skills rather than be distracted, concerned over existing skills you should already know.
As an example, it is much easier to teach someone to use a stage cylinder, if they are already comfortable with removing a regulator from their mouth, replacing it and purging it (a basic skill). If they are uncomfortable with this element, they are not ready to progress.
Much later. You have a balance of practical experience, theoretical knowledge and practical skill to discuss and debate new practices and engage in less familiar diving, or develop new techniques to overcome particular difficulties.
But even at this level, there are things I would hope that you understand and foolhardy to attempt without further tuition.
By this i mean real practical tuition by an experienced instructor in this activity.
To me, the most obvious one here is cave/cavern diving.
I have many years of diving experience, practical skills and knowledge. I dive OC, CCR, mixed gas and instruct. BUT, if I started any cave or cavern diving I would want PROPER tuition. Yes I can research it, I can apply knowledge I already have. None of this substitutes for proper instruction by an individual that does this type of diving, understands the rules and the why's. I can debate the rules - using my existing knowledge, and learn why certain practices are cast in stone.
There are many lessons that have been hard earned. There are many standard practices that we now apply to our diving, and teach our students. What causes great sadness, is when new divers fail to absorb these practices that have been so hard earned, or ignore them; with the potential result of serious injury or loss of life.
Like many other things in life, diving is about weighing risk and reward.
There are significant difference in terms of risk when comparing say a shallow reef dive in tropical conditions, to those experienced when doing a deep mixed gas dive in temperate waters 10 miles off shore on a 80 year wreck.
Understanding the risk, and how to mitigate it is part of the education.