They already do this surely? I would think to implement high quality Bayesian type spam indexing, it's much the same.
They parse over header all the time. All mail providers do to implement procmail type functions. They parse body because they support complex boolean logic over string search.
I get it: this feels like a meta step "upward" but really, I am unsure it is. I am also of course like you concerned. It's my mail too.