The counter point to this, is that I know of a family member went to the ER after passing out (after the 2nd incident) and was able to diagnose a life threatening condition. If they had a healthcare plan like this, they would have probably not gotten care and would be at risk, because the only reason the diagnosis happened was due to symptoms that only show up immediately after their incident.
The risk here is having patients doing their own triaging. If the insurance company really wants to reduce costs, they can partner with a network of ERs who commit to triaging and transferring to lower cost providers if the issue is not an emergency. The patient is not qualified to make that decision.
I worked at a health tech company where we analyzed bringing down costs through claims data, I can tell you that there are actually hundreds of ways insurance companies can reduce costs that won't risk patient safety, but do not. For example, there are billing mistakes all the time, but insurers do not give a crap. We tried building features to help identify billing mistakes but we never could get insurers to care about it. The amount of times I saw insurers undermine patient safety for "costs" was staggering so I'm really skeptical that the insurers are doing the right thing here. As another example, we saw insurers build "Centers of Excellence" and push patients towards taking care there. Basically what they did was find crappy hospital systems who were willing to take lower rates and they would tailor their insurance plan to push patients that way. Unfortunately when we analyzed claims and outcomes we found these Centers of "Excellence" actually had way worse patient outcomes. We raised this point with the insurers and again, they did not give a crap.