One thing which is annoying in the present demo is that I normally edit things by groups, say I change the font of the x axis title, and the next thing i want to do is to change the font of the y axis.
Without exaggerating, I can say that what you already have is a huge boost in using TAChart. When I compare Laz 2.0 and now Laz 2.1 + your demo files, it is like upgrading from a bicycle to a motorbike. There is now an existing engine and you don't have to do everything on your own.
In the past I got a lot of criticism because the charts were not as handy as e.g. programs codes with .Net or Qt. Today I presented my first version of the program to two colleagues and they said, that is exactly what we need. I was even surprized to get this positive feedback.
And also the existing visualization programs we use, use the same method as you do in the demo - click on the axis you need to change. Only in rare cases users really need to change all axes. And for these cases, one can handle this at runtime. I e.g. have a button in my app with which the users can change the style of all line series in the chart because this was requested by users.
As you wrote with your reference to TeeChart, you cannot please every potential use case or you end up in a huge and unhandy tool.
So in fact your demo code is exactly what average coders needs - the basics are covered and one can fine-tune it, add or remove features. And having your existing code saves many hours of coding and testing! So please consider providing the existing demo code as package for TAChart. I bet that I am not the only one who would love it.