Sol, what plan are you on, if you don't mind me asking?
My employer subsidized HDHP has a ~3k deductible and ~7k out of pocket maximum, for which we pay ~3700/yr in premiums. My employer also pays another $11k/yr in employer contributions.
In an average year, the insurance company collects $14,700 in total premiums for my family, and pays out approximately $1500 for preventative care visits for five healthy people. They also put $1500 in my HSA.
Total costs to me, my premiums plus my OOP costs, minus their HSA passthrough deposits, minus the tax savings in my marginal tax bracket for a maxed out HSA, are about $2500/year to insure the five of us.
As soon as one of my kids breaks a bone or has other major expenses, we'll blow though the deductible and then hit that OOP max, and will spend about $10,000/year to insure the five of us. This will be about double what we were previously paying for more traditional insurance.
So basically, the HDHP (because of the HSA) is cheaper for us as long as we stay healthy, and more expensive if someone gets sick or injured. We pay 100% of our costs for every urgent care or pediatrician visit that is not preventative care. So we pay cash up front for all routine care costs, which is thousands of dollars per year, because we are wealthy enough to cashflown those expenses in order to get the tax benefits later.
This works great for us. It would be terrible for most Americans.