Physicians groups, insurance companies and biomedical ethics groups aren't really hip to this idea because patient self-testing bloodwork may open pandoras box to a lot of unnecessary expenses, especially if the patient is trying to bill this through their insurance. False positives can and do happen, and they lead to unwarranted appointments, specialist visits, exploratory surgeries, etc. Other reasons physician groups are opposed to it is because they view it as profiting off people who are hypochondriacs, and a huge amount of the customers would probably be drug abusers and steroid users. Most likely, people who would go and do their own blood work are the system's "super ultilizers" and they are the ones who are already costing the insurance companies and the states $3-4 million per patient per year in healthcare expenses. It's not uncommon to have a fibro/rheumatoid arthritis/hypochondriac patient who bills $10 million per year. If these people go to the ER and cost 3k per visit every time they can't fall asleep and have anxiety (~12x per month), imagine how often they might want to go and run their own bloodwork.
Not being able to order our own labs as patients is the reason there are moral objections to for-profit hospitals selling "full body scans" and dermatologists doing unwarranted full body mole checks. Generally the proper guidelines is to only administer testing when you suspect that something is wrong.