No, you don't typically have to stake irises, but if they are growing in partial shade they sometimes need staking. Older cultivars can also be weak-stalked, and a few modern ones. like Victoria Falls, are known for falling over.

Less water and more sun might help, or it might be a fault of the iris.

Some plants get floppy if they get too much water and fertilizer. Irises are very drought tolerant and don't require a lot of fertilizer. I grow them in the leanest and driest parts of the front gardens and they do well under those conditions, and perhaps it makes the stalks stronger.

I usually end up having to stake a few though, because they are in a very windy location and once the blooms come out they act like wind sails. I use the green wire stakes with the little loop at the top.

One kind of mine fell over so badly a stalk snapped at the bottom where it connected to the rhizome. It didn't do that until I ran a sprinkler for nearly half an hour, though, and it's been suggested that the weight of the water on the flowers was too much for the long tall stem, heavy as it was! So.... I got a soaker hose to wind through the bed for watering from now on. Also lets me direct the water a little more accurately (tall wide things were blocking smaller items behind them), so the whole bed should be happier from now on. Now I just need some mulch to cover up the hose!