"Capitalism and neoliberalism are not mutually exclusive in any way."
In our political reality, they are. True capitalism would eschew monopolies in favor of open market competition. Our system is state-sponsored markets with regulations more designed to protect monopolies against competition than to protect consumers.
A good example of this is Medicare. Insurance actuarial showed that boomers threatened the industry with extreme future rate hikes that would have impacted both insurance and healthcare providers. Ditto with VA and Medicaid coverage. The numbers simply didn't crunch in favor of insurance without socialization of the highest-cost sectors.
Medicare was a solution that took boomers off the insurance roles just as their projected costs went off the chart, protecting profitability. Even with the overwhelming support of the program at the time, socialization was not 100% and insurance was still required if beneficiaries were to be protected from extreme financial risk.
The government, which neither needs nor uses "revenue" to provide benefits, interjected payroll deductions and copays, deductibles, etc. into that socialization that did nothing except draw down the spending power of the beneficiaries. In a true capitalist system the state would create money and distribute it directly to consumers, not corral them into its predermined markets.