You should look into reading the book Health Communism, I'm currently working through it, but the argument in so many words presented by the authors is, "Yes", but likely not for the reasons you think.

The "welfare" state is something that arises through the contradiction between capitalism and health itself. Health under capitalism acts as capitalism's host, but because of that fact, health takes on the important characteristic as capitalism's key vulnerability. In order for there to be productivity, capitalism needs to identify and maintain productive bodies, and in the same breath, claims that doing so is in no way a requirement under capitalism. This contradiction explains why health systems both new and yet-to-be implemented under capitalism are so desperately attacked.

Health, according to the authors, has no fixed meaning; it is fluid. They describe it as a "race/class-stratified matrix" defined by artificial scarcity and negation; non-cancerous, non-disabled, etc. The capitalist definition of health ultimately is one where a person must be productive, normative, and able to buy health. They draw on the works of the Socialist Patient's Collective (SPK), who described "Health" to be a purely ideological ideal, a "biological, fascist fantasy" that conceals the social conditions of illness. The goal of the book is to reclaim the notion of Health from this fantasy, under the concept they call Health Communism.

They argue that Health under capitalism is used to divide populations. Capitalism separates people into deserving and undeserving lots. Separate workers from the "surplus" (those who have been biologically certified unfit to work). This surplus population then becomes marked for "extractive abandonment", then framed as eugenic or debt burdens to gut and block reforms. They argue that to abolish capitalism, we must shatter the worker/surplus binary, and center the surplus population in our struggle. Health Communism then becomes a goal where people are not simply provided the care they need (since, "need" is often decided by the welfare state), to all care for all people. It must go beyond equitable redistribution or state-provided "socialized medicine" inside of capitalism. They argue for an internationalist, anti-austerity, anti-border, approach that demands a radical abundance of care.

As others have pointed out, socialized medicine within capitalism is insufficient. The NHS, Canadian Medicare, etc. remain capitalist and imperialist systems. They do not exist as "islands of socialism" within capitalism. For this reason, they state that Medicare for All is not enough by itself and that health insurance companies are not in the business of providing care but instead simply financial risk-management institutions with no place in society.

They go on to define health as broader than simply healthcare. Housing, clean air, water, sanitation, social supports, in-home aid, and a livable planet are all healthcare, alongside traditional care. These European-style social democracies are the shining example of the limitations of healthcare under capitalism. They support themselves through imperialism, gatekeep care through the debt/waste frame, divide the proletariate into "productive" and "unproductive" masses, and use these tools of clasification as means of labor discipline. The threat of becoming "unproductive" looms over us all.

There have been countless stories in the past few years that highlight these points. In the UK, Jodey Whiting was housebound with chronic pain when the DWP judged her "fit to work" and stopped her benefits; she took her life two weeks later, and a coroner ruled the wrongful withdrawal was "the trigger." Errol Graham starved to death eight months after his disability benefits were stopped. Philippa Day was found dead with a letter beside her refusing her a home assessment visit. Laura Winham lay dead in her flat for three years after her benefits were cut off. Academic research has linked the work capability assessment to 590 suicides in a single three-year period. These are not anomalies. They are the predictable output of a system that recertifies the surplus as "capable" to make good on its promise to eliminate "waste" and cut down on "debt". The "waste" that they eliminate, quite literally, are people.

The current incarnation of healthcare under capitalism is obviously insufficient. We should not be championing its destruction, by following the lead of rightists hellbent on subsuming the entire system into private hands. However, I also cannot say that the system that should replace it would look anything like the systems that exist today. We're talking about a system where people simply get cared for; no questions asked, no qualifications necessary, no need to be certified as needing that care. We need a more radical demand, one where "we are not basing the value of human life on one's willingness or ability to be productive within the current political economy."