We never really back up and say ‘did you REALLY get that part, because you’re going to NEED it for the next 14 years?’. I can remember I was sick for multiple weeks when we were learning division. I came back, and we were already onto the next topic, and it was just assumed I knew it. Now, I was super-lucky, in that I understood multiplication well enough to puzzle it out. Not every student cares, especially when they are like 8 years old. Just want to learn it enough to pass and be done with Math. ‘What do you mean I have more Math next year too???’
As soon as you miss a single step in the mathematics education train, well, you’re going to be hating math for the rest of your schooling. It’s a series of incremental building blocks, but we never double check that each student really has each piece.
At the risk of sounding silly - Instead of focusing on burning the solids, boil the water. Water boils at 100C, at which point the water vapor should separate and leave all the solids behind. Then capture the vapors and condense it back down into clean water. Now, if you later want to incinerate the leftover solids, sure, go for it, fire’s always cool in my book.
I’ll add, simply boiling water is energy intensive. What you are proposing probably won’t work at any scale.