v2 Ay is too fast for the sharingan to track, so when Obito attempts to warp the Third Raikage, Ay can blitz Obito while he is warping.
Because izanagi lets obito tank an attack from the Ay, thus allowing him to warp them away or place them in a genjutsu.
He doesn't need to track him in order to touch him, intangibility deals with the attacks that could decapitate him while he could tank any attacks [from the 3rd] aimed at his torso.
Then there's the fact that these guys can't sense, so a surprise warp from behind is easily achievable since minato didn't notice obito was behind him until after the fact, & that wasn't even his fastest warp time.
I also need scans of obito being blitzed while warping because that's untrue as well. The only times obito has ever been damaged while warping someone was when he chose to touch torune & lost his arm, & the time where he had to warp konan + her paper wings filled with bombs [also a head on, cocky warp].
Ay isn't reacting to a surprise blitz warp, not when he has no idea when or from where obito could appear. 3rd raikage gets warped before Ay would even notice.
Ay will then see Obito respawn and realize that he's using a jutsu to make him immortal.
Obito can choose when & where to respawn, he respawned right behind konan after the explosion. All he has to do is either respawn right behind ay when his guard is down or respawn a significant distance away & warp behind him. Ay isn't finding out about izanagi.
Ay easily outlasts him in that 10 minutes and then goes in for the kill,
Ay isn't outlasting anything, he's going to blindly attack obito through blitzes, & each time he does it either gets phased through or tanked depending on where he tries to hit him.
Izanagi can be used
after the battle even takes place, 5-10 minutes after ay thinks he killed obito & lowers his guard he can still be attacked. Obito doesn't need to use izanagi during the battle, if the suicide warp doesn't work then he plays possum until they do lower their guard.
whereupon Obito gets gang banged from both dimensions by Ay and the Third Raikage.
Obito can eject people from his dimension, once the 3rd gets warped obito teleports to another location & dumps him there.
Also how on earth are the thick-headed raikage going to even figure out how obito's ability works? They aren't going to be looking for the floating body parts, & if obito simply moves locations then they'd never figure it out.