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

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.