You got it right. Thanks for getting some sense out of my broken English.

As you pointed out this is not the first time, a would add that it is also an escalating process proportional to the population and progres/regress(depending on personal view on what constitutes the former) of the civilization. I can speculate that this process reached its "critical mass" by the end of the 19th century causing a world war which led to the complete restructuring of the world including the Art world.
The belief system has changed permanently "announcing" the new setup through turmoil of the WW1 and Russian Revolution.
Artist, in my opinion, is the creature that senses such cataclysms and reacts to it, BEFORE the actual events begin to happen. However, society is conservative, by nature, and most of the time it has to be "taken by surprise" in order to except new in Art. Avant-garde artists used the War and R. Revolution to manifest this change. In my opinion, the common assumption that the WW1 caused the change in art is incorrect. The change in belief system did and it happened before the war. The war was an opporunity(for the artists) for the proclamation of such with their idea of the visual language for the "updated world" (In my thoughts I would go even further and say that artists, with their "doing" and "not doing", are the ones that caused the change in the belief system and all of the concequences including the war and revolution. but this is a different subject altogether)

Surmising: You say "It is their world we live in.", that is correct, but it is also our world and the world of everyone that has been before.
I would be very burdened indeed if there would be now Mondrian. His color combinations taught me a great deal and influenced my view on the use of color, broadening it conciderably. (ironically one of my paintings is hang next to his at my friends house in Finland, this "hanging" introduced me to his work)

This is why I draw the distinction (not sure if I use this word in the correct context) between Art and Decoration. Artist should make it clear for him/her self which one of the two is primary, because this two do not mix but coexists. Choosing the primer (art) the one submits to the "loss of identity" in the realm of rational world and time, in exchange for the power to manipulate the consciousness and the consequence. Most of the time the later (consequence) is left out, since it requires a titanic effort - hence the "lazy" in my previous post.

Decoration uses the product of art (whatever that is) transforming it into the "stable" form (period, style, etc.)

So it is nether "their" world, nether it's "ours". It is the world of power and the abyss of consequence. The only guide that artist can have is the same abyss and power that he/she has to be guided through.