Why couldn't Ocean's team show Benedict the live feed? Why was the recording needed?

There are a few reasons why they would want to show Terry a video of being robbed, instead of showing him the live feed (or essentially feeding him a video of an empty vault):

1. They had to have a way of getting out of the vault in a plausible way. The fact that they managed to get in is one thing - but they also needed to walk out with a LOT of money. They couldn't go back the way Danny and Linus came, because they would have to go via the elevator shaft (which was rigged with sensors) and then via the hallways to get out the door (which have a ton of other cameras they didn't have access to). The only way they could do that was to have a situation where a SWAT team was called in; nobody was about to take a head count of how many SWAT members went in and how many went out.

2. They didn't want to show Danny being part of the group robbing the vault, because they wanted to allow for plausible deniability for him (remember, Terry still thought he was being beat up by Bruiser - though how he [or the two guards outside the door] could believe he was still getting a beating even during the blackout is a MAJOR plot hole). Thus, they didn't want to risk having Terry see Danny's face on the video (all Terry knew was that Danny had 'something to do' with the robbery - that could just as easily have just been in the planning).

3. Finally, as to why they didn't wear masks in the video - that was essentially a big "fuck you" to Terry. It was like "We don't care if you see our faces or not. We're MASTER thieves, and we don't go about robbing you wearing a bunch of masks" (unless it's needed to get away in a SWAT uniform lol).

Because only two of them actually broke into the vault, but to really threaten Terry, they need him to believe that they all broke into the vault and can do a lot of damage. And of course they need to fake a footage of SWAT attack later...

This is my understanding of how the robbery took place. Rusty gives Benedict the option of either loosing half the money secretly or loosing the entire money publicly. They were going to take half the money, leaving the other half as hostage, booby trapped. At least that's what they made Benedict believe.

In the recording of the tape, they were shown packing only half the money while Danny and Yen were actually packing everything. When the swat team arrives, they bring bags filled with the fliers for hookers which they then blew. So it wasn't until the swat team was out of the hotel that they find out that they had actually been robbed of the entire amount.

The entire heist could have been run from the mock up cameras....with Terry calling in SWAT, and Ocean’s team coming in in SWAT gear and taking the money.

There was one problem.

'The vault doors and the time table'

If they had just showed Terry a mock up and he called SWAT, there would be no way for Danny and his team to enter the VOLT. Sure the could use C4, but you’d ruin the money as well.

So the movie is correct that they needed Yen on the inside to place precision explosives, as well as Danny and Linus in to bag the money up-remember Terry went down to the vault within 2 minutes.

So in short, pulling the heist would be impossible without entering the real vault.

When the swat team and Benedict showed up at the vault after the explosives were detonated, there were no suspects in the vault and no clear way of how they got out (because the three people had joined the swat team). They made the recording so that when Benedict found out it was a recording, it was an explanation to why there were no suspects as he thought that he was not getting robbed at the same time that he saw the recording.

Of course this could just be a stroke of luck as the Belagio inscribed on the floor had been installed earlier that week (Benedict says: "It was installed on Tuesday" when talking to Walsh). They could have been unaware of this and not included it in the replica of the vault, or they could have been aware of it and purposely not included it so that Benedict would notice. It is a small plot hole but not as major as the mystery of how the fliers got into the vault that were sent up in the elevator and into the van.

They steal all the money. After Brad Pitt has eaten all his sandwiches, they play a video of themselves mucking about in their own pretend vault. But in real life they already have the money anyway. And then the big man who is pretending punches George Clooney, and everyone is left wondering what has just happened.