There SHOULD be the same incintive in private health care like the US to also lower costs. but when we voted in the ACA (Obamacare) there was a well meaning clause that said insurers had to spend 85% of their premiums on care. That should also re-inforce the cost savings part, but then the largest companies started buying Pharmacies, Pharmacy Benefit Managers, Doctors offices, and even whole Hospitals.
Now they can still spend 85% of the INSURANCE premiums on care, but then those costs are going to their other divisions which can raise prices at will, and make massive profits for the whole group.