All summoning techniques require a contract of some kind, edo tensei shouldn't be any different. Plus you are forgetting that it doesn't just on the fly summon people, a long ritual needs to be performed first which also needs a living sacrifice (host body). Then after the summoning you'd need those little talismen to assume full control.

So even if sharingan could somehow copy edo tensei, it would still be pointless cause the jutsu is useless without the ritual.
Itachi is there cause he's a powerful genjutsu user, that's obviously the way to get an edo tensei user to stop the jutsu.