Again, if you are busy dying, you (or, more likely, the bystander who calls EMS on your behalf) do not have time to check how much the bill will be, or who has the best response time to your location at that moment, or the best equipment, or the best training.
Again, if people are doing it cheaper, how could a 13k per ride company stay in business? 911 services would have to be steering them to an insanely bloated expensive company. That wouldn't happen. Competition brings better service and much cheaper prices, always does, without exception.
There's a distinction between 911 emergency ambulance service (respond to people calling 911) and interfacility transfer service (transfer stable patients between hospitals and medical facilities).
When you are an ordinary person calling 911, you can't meaningfully shop around in that emergency situation. The competition that exists is between the possible organizations you local government could contract to run the system. The safety regulations and medical standards they set are part of them choosing what they feel is the best "deal" for their population. (In some places, all 911 calls are run by public fire departments; in others, the government contracts with private companies.)
At the IFT level, again it's not generally possible for patients to choose their service, because (as explained in the article) ambulance services inherently need extensive infrastructure with large fixed costs at every location they serve. You're not going to fit 20 ambulances from 20 competing companies in one hospital's ambulance bay, and those 20 competitors aren't going to be able to afford to pay employees to sit around for hours at that hospital on the off chance that maybe today patients will pick them and not the other guy. The costs for the ambulance company are not primarily per-call, most of the expense is to stand ready for a call whether it happens or not. Instead, competition generally happens when the hospital chooses which ambulance service(s) to contract with.
Again, as I keep explaining, if companies were free to compete then even 911 is not going to redirect you to a 13k ambulance service. Why would they unless they are getting payoffs. It doesn't cost anywhere near that to transport you.
True, but again, if people were free to compete why would the hospital go with a 13k option. If people had any choice in the matter, which many times they don't due to regulations, then they would pick a cheaper option.