That wood and charred elements could be who knows how old? Ridiculous to think dating of charcoal means how old the people using the charcoal are.
The archeologist who investigate these things are looking at all of the available evidence to come to sound conclusions.
Not only are the drawings dated, but also the burned woof within a fire pit are dated.
Usually, but not always, stone tools will also be located in these caves. Our ancestors had "styles" just as we do today. The tools are found in various strata (layers of sediments) that have built up over thousands of years. Each different strata can be dated through dating the various organic materials in those layers. That gives the date of the stone tool plus or minus 20 years found within different layers.
Humans tend to come up with the same "styles" over a large area either through trade, exposure to others or just thinking the same way.
So, when I find an 11,000 uear old paleo spear point on my lake, I do not need to go through the process of dating because it has already been done on the same style in many other places.
It's kind of like finding a Ford