A lot of old insulation can stay right where it is. If it's dry, clean and doesn't smell, new insulation can go on top, and paying to pull good material is money better spent sealing gaps or adding depth. I only recommend removal when it's soaked, moldy, smells bad or has rodent mess in it, because at that point the old layer is the problem.
The same thinking applies below the floor and inside the walls. In a crawl space, old batts, the pre-cut blanket rolls, often sag, pick up moisture and fall, and pulling those is usually the first step of crawl space insulation. Walls hide their insulation, so we only open them for a real reason, and wall insulation covers what goes back in.
Anything that looks like old vermiculite stays put. We leave it alone, point you to a separate asbestos specialist for the licensing reason above, and pick up the rest of the job once that's sorted. It's not something I'll eyeball and then go ahead with anyway, because the cost of guessing wrong lands on your family.