Izuku's sure Shouto can keep the ice from melting- he's seen how long his ice can last. But doing this one by one- it would probably take them the entire day, and they might not need to eat or sleep but he'd hate to deprive them of that.

There's a pause as he considers, "It's better than doing it one by one. I trust you."

Kido's powers are entirely under her control, if she thinks she can bring just a few of them to him, then he believes her. They'll be able to clear the cage much quicker if it works the way she's intending.