We just went through this. My new job has pretty crappy insurance with a $4k deductible per person. As with all insurance you play the risk game - we generally quite healthy and going to the next tier of insurance would cost over $4k/year in deductions so we figured we'd roll with it. Well derp of course something came up and we tore through that $4k pretty quick. Through the course of it though we asked the emergency room and the procedure place about using the insurance vs not and two weird things came up:
1. the office/billing people balked at the idea of choosing not to use the insurance that we had even after we explained it. one claimed it was illegal.
2. with all of the sub-departmental billing in these places everyone ended up having a different policy - the procedure was cheaper by 10% without insurance, the anesthesiologist was twice as much. the lab work was more expensive, the ER stay wasn't. totally

ing bonkers. and of course spending 4-6 hours in the ER with an MRI + bloodwork with no benefit to us (i.e. no problem found and sent on our way) was about $50k on paper.