I mostly agree with you, but wanted to note that the money they spend doesn't get "burnt". Spent money gets just moved around, it isn't destroyed. And a significant part of the money spent on climbing Everest stays in Nepal - an extremely poor country - where it can maybe do some good.
The goal of rocket reusability is to get the fraction of launch costs that is spent on burning stuff as close to 100% as possible. In a somewhat literal way, by making launches cheaper they are making "rocketry is burning money" more true, not less.
In a strictly literal interpretation of an entirely figurative figure of speech.
The money might literal be burnt in the form of fuel, but it will be only the cost of the fuel. Modern and older rockets had to burn that and effectively burn all the other disposable costs, like the whole rocket and every piece of gear sent up. The situation is certainly being improved by these new innovators, and that is the point that was trying to be made and it is highly likely that you knew that.
Edit: Typos