This is always extra annoying because it might be a false savings to pay cash there. Let's say your MRI says you need a $5500 procedure, and your plan's deductible is $3000, 90% coverage after, and out of pocket max is $6000, and there's nothing else you've spent on the plan this year.

Pay $800 for MRI with insurance, you'll then pay $2200 for the procedure to hit the deductible + 10% of the remaining $3300, so $2530 total for the procedure. $3330 total for the year between the two things.

Pay $600 cash for MRI, you'll then pay $3000 for the procedure to hit the deductible, and 10% of the remaining $2000, so $3200 total for the procedure. Now you've paid $3800 total, so you've spent $470 more despite the MRI being "cheaper"!

If you have other expenses so your out of pocket max comes into play, that difference approaches the full $600.

Do you folks have to perform these calculations every time someone in your family gets sick or injured?

Yes, unfortunately so. You have to play the stupid game of "expected medical expenses".

For example, am I going to do something major like have a baby this year. Then yes it probably makes more sense to get me to my deductible and pay the extra money to go with insurance. Or if you (or someone on your plan) has an ongoing medical issue where you know you will meet your deductible. Or on the flip side, I met my deductible one year and was going to physical therapy. Since I met my deductible the physical therapy visits were cheap, but going in to the next calendar year now my deductible reset. Could I have used more PT? Maybe, but the visits were about to be 5x more expensive.

But "expected medical expenses" is just the dumbest thing.

Usually no, most people just use doctor-suggested or in-insurance-network providers and billing because it's easier than calling multiple places and hyper-optimizing on the math.

But we have to pay the bills after the insurance company does the calculation, which often results in annoying surprises.

The better your insurance, the less nasty surprises, which largely in the US means "the better you're paid, the less you have to pay out of pocket for health expenses" which is a nasty thing because then the people most likely to be hit with a big bill are those who can least afford it.

No. I know that my total expense in a given year will never exceed $X (Premium + out-of-pocket max). Worrying about every single transaction is not worth it.