Arguably this is true for nearly all medical conditions - prompt treatment helps, at least if there’s any effective treatment, either by avoiding a worsening condition or resolving the problem sooner and leading to better quality of life (barring edge cases like risks from over-testing for conditions you might but don’t actually have). Cancer is a very obvious case for this, but it’s true of joint replacements, organ transplants, getting your high blood pressure or diabetes under control, etc, etc.
To a large extent, all these HMOs and government run managed care programs run you through hoops to get your problem actually treated by the appropriate specialist are doing cost control at the expense of the patient’s health. Look at the VA for a classic and fairly bad example - hidden waiting lists and interminable delays before you can get seen, etc. if you were paying full price out of pocket for the whole thing, someone in a free market (or even the current US system) would be happy see you promptly. It’s only because of all these intermediaries like the government single payer provider or private insurance companies with conflicts of interest result in these imposed delays, multiple required referrals, deductibles to discourage seeking treatment, etc. none of that is good for the patient, but the party paying cares more about their profit or cost control, and doesn’t have much incentive (aside from maybe shame or a little bad PR) to get you good prompt health outcomes.