Well, it's this little thing called Game Freak Logic.
Theoretically, yes, Mew should have access to all Pokémon moves. However, logically, it can't. Mew only has 100 levels. There is no possible way for Mew to learn every single Pokémon move in 100 levels. To fix this, GF simply gave it access to every TM, HM and Move Tutor move ever. Also, it doesn't really make sense to give one Pokémon the signature move of another completely unrelated Pokémon. I know that Entei got Sacred Fire, but let's be real, he at least looks like he should be able to use Sacred Fire. Can you imagine tiny little Mew devastating everything with Dragon Ascent?
P.S. Don't bring up the fact that Darkrai got the signature moves of the Sinnoh Legends, that was just something for fans to drool over.