Many trees do have some roots that go deeper. These are older, established trees, and the ultimate depth can still vary greatly.
Very deep roots occur more commonly with certain species and in certain climates and soils, usually drier climates and deeper soils.
Most of the time, trees with deep roots will be accessing water from the local water table and will no longer require irrigation. I suppose that could change due to climate change and severe droughts, but then there won't always be irrigation water available anyway.