Because your body needs a mineral structure, like bones, to leave fossils. Bugs, plants... jellyfish, they don't leave fossils as we know them (only marks) because their entire bodies degrade; as such, it makes much more sense to think that rock-type pokemon, with their harder, already mineral-like structure could withstand the fossilization process enough to leave more than a mark, and to protect their DNA inside their remains.
Sure, there were all kinds of pokemon in pokemon prehistory, probably, but only a few left fossils, just like in our world.
And lance also used gyarados and charizard, before it got a dragon-fire mega (and let's be honest, that was simply audience pandering; the true charizard mega is mega charizard Y).
And above all, don't forget that in GF's design guidelines, strong reptiles and dinosaurs (such as pterodactyls) are covered under the Dragon type (much like a certain non-dragon fire dragon).
Well, more Pokémon could be preserved in ambar and so DNA would be found without what's left being just bones! It's only lack of thought by GF because they could go with more "fossils" obtained from ambar.
You do have a point about Charizard.