The whole point of ME is that you trade sanity (and the abilities you have) for power.
If you could use your normal powers ANYWAY, then how would it even be a drawback. Use ME for power, turn it off and use your skills when you can.
But nobody does that, probably because you can't. I mean, Kariya could have had Lancelot not insane and out of control which would have helped him in a lot of situations.
Plus, it's weaved right into the summoning incantations, which kind of sounds like it's built into the way the Servant is going to operate for the duration of their summoning.