Why didn't they just use a fossil re-generator for Mew?

My question is this: Why, if the scientists in Cinnabar Island can regenerate a fossil from a dome or a shell, or especially if the Hoenn scientists can regenerate an entire pokemon from a claw or a root fossil, why didn't they just do that with the Mew fossil that was used to create Mewtwo? Or do I not remember the story correctly..?

I am not quite sure what you mean here, but the way I remember it, Mew already "existed"--people just started sighting it and it snowballed from there.

However, to try answering your question, I can only guess legendaries (or perhaps even Mew in particular) are simply too powerful to be brought back with mere scientific technology. At least not without a catalyst.

Or Pokémon canon is just incredibly inconsistent.

Like Pure Evil Groudon?