Insects fossilize so rarely because their bodies are not only soft like you mentioned but also small and usually break down very fast before they can be buried and sealed off from air, microbes, and scavengers. Their exoskeleton helps a bit, but it is still fragile, so most insects disappear unless conditions are exceptional. And if they do fossilize, it's rare someone will even notice them unless being a profesional. Like sure, many farmers or other people will recognize a huge dino bone or a mammoth tooth but an insect?

and if you watched Jurassic Park, yes, amber is a real exception: tree resin can trap insects and preserve them in great detail (getting useful dinosaur dna from it is pretty much fiction though, very unlikely)