Why use antifreeze in warm climates?

Yes, you still need to use antifreeze because it contains compounds that protect your cooling system from rust.

See a photo of a rusty radiator.

Over time, rust will begin to block the small passages in the system, especially in the radiator itself. At a minimum, rust will reduce the efficiency of the cooling system which could make your car run hot. And when the rust gets through to the outside world, the radiator begins to leak.

This will happen eventually with almost any car - but using antifreeze with rust-inhibitors will slow the process down and buy you a few extra years.