You put a lot of thought into these things, here are my thoughts on various points you bring up:
Make healthcare prices more visible. I completely agree with this but to understand why they are not we have to think about how healthcare prices are determined. There is an annual (maybe bi-annual?) conference where some hundreds of physicians prominent in their branches of medicine and known as experts get together and discuss the appropriate costs and thus fair prices to be charged for just about any medical procedure that can possibly be billed for. The result of this conference is the price book for what Medicare will pay for anything. The medical community in its entirety basically uses this as their starting template for what private individuals and insurance companies should pay for their services as well. So some handful of people are setting some ridiculous prices year after year that are the very epicenter of rising costs. I bet you are already thinking in your head the major problem here. A handful of Gynecology physicians basically get together and decide what a fair price is for Medicare to pay them, it is the mother of conflict of interests. The higher price they set the more money they stand to make, especially if those physicians happen to be known as experts in a rare type of procedure that few know. They can come up with some extraordinary number and know people will come across the country to see them personally if one of those Gynecology experts doesn't happen to live in their city. Other factors for why they decide on a higher price usually have nothing to do with the procedure itself and sometimes if the insurance company decides to stop paying a proper amount for various medical supplies that are used in other procedures. They will often up charge with the anticipation that insurance companies will try to bilk them in other areas. The problem is a difficult one to solve especially since Medicare to be fair needs to know a fair market price and relies on experts in the field to tell them, so it really is the medical community in this country that really takes the lions share of blame here. How we solve that I don't know.
Send people a check and they can shop around. Assuming we solve the price transparency issue and rising costs, this might help to curb medical costs even more. I think market based healthcare can really only work if it is single payer to the patient and let them decide where to spend that money.
People abuse Emergency Rooms, they are always in the Red. Yes but if we had true single payer and people could actually get paid or reimbursed for non emergency healthcare then this problem mostly solves itself. Right now many hospitals pretty ingeniously recover a large chunk of that money lost in giving free and charity care to poor and disenfranchised peoples. They write off those losses on their books as charitable donations. If they can accumulate enough of these "charities" then they qualify for Non-Profit corporation status which gives them a slew of tax benefits that sometimes more than make up any operating losses in their emergency room.
Why don't people talk to doctors online and save money and time? This is already a thing and there are a lot of startups right now trying to solve this problem in an innovative way. People can post their symptoms and be connected with a physician or PA that can talk with them one on one and try to come up with a diagnosis. Perscriptions can be automatically filed and sent to your preferred pharmacy when applicable. Last I checked though, insurance won't pay for stuff like this until Medicare adds it to their price book and we come full circle back to the physician conference.