We also need to make sure the audience isn't rigged up to explosives.

I'm thinking that the second we're all engaged, before they have a chance to react, we have the Flash check the audience and their seats to make sure they didn't leave us a little surprise -- and dismantle it all at superspeed if they did. Cortana said she can shield them but by the time we get there, they'll have had time to wire them up to explode to kingdom come.

They wouldn't be above setting something up that puts the hostages in the audience in danger.