In the US, if you make a lot, are covered by a work retirement account or you contribute to a Roth, you can't deduct traditional ira contributions right?

So that money gets added to the rest of your traditional ira monies right? and then when you hit retirement age, you have to pay income level taxes on deductions on that already post tax money right?

Why get taxed twice? What's the benefit? +Not being able to touch it til retirement age.