... well, too late, because your insurance was chosen and paid for by your employer (if you have one), and your clinical decisions were made for you. Oh, and if you try to change insurers you will be denied coverage for your "pre-existing condition".
The UK is far from perfect, but it does the basics well (antibiotics, contraceptives, emergency care, insulin). And there's zero risk of it making your state worse by bankrupting you.
And for those who want faster care, private insurance is still an option. It's just that: an option. Not something that people have to desperately scramble for.
Then when you need to make a claim you discover that Company B gave a good deal because in the fine print they added exclusions that result in your claim being rejected for some arbitrary reason. So yes, in the long term the competitive landscape works as word gets out that Company B's plan is garbage, but in the short term you are forced into personal bankruptcy or a worse health outcome.
You really trust the government to take care of you? How blind are you? The UK government wasted £12 billion of taxpayer money on an abandoned IT system.