The idea of sustainable, consensual equity-in-diversity, of democratic commonwealth, is not a "mix" but a coherent political vantage, a political being democratic processes experimentally implement and a political becoming at which democratic struggles aim.
What tend to be called "capitalism" and "socialism" are, it seems to me, very much to the contrary, historically unrealized and logically unrealizable derangements of either the diversity dimension or of the equity dimension of the democratic value of equity-in-diversity. That is to say, it is the prior conceptions of "capitalism" and "socialism" that seem to me to be mixed, if anything, historical and practical misapprehensions and dodgy implementations of consensual multiculture, democratized association, sustainable commonwealth.
And hence, the contractual arrangements to which moral cases for capitalism are devoted will always depend for their actual legibility as consent on a substantial provision of general welfare and socialization of common and public goods typically denominated socialism from those argumentative vantages, just as anti-authoritarian cases for (eg, democratic) socialism will inevitably allow for differences of preference and outcome typically denominated capitalism from those argumentative vantages. This is not because modern societies have been mixes of socialism and capitalism historically, I think, but because the democratizing struggle for sustainable equity-in-diversity is the political substance from which capitalist and socialist abstractions are strained and deranged in the first place.
Again, I think it is what passes for capitalism and socialism in thought that is mixed up, the "mixed economy" in practice is not a mixture of these two derangements from good sense.
Democracy is the idea that people should have a say in the public decisions that affect them -- and that includes having a say in matters such as who are these people? what constitutes a proper say? of what does the public actually consist? and just who is affected by what that demands an accounting? There is no single regulative or ideal democratic form, but only endless efforts at implementing and struggling over the idea that people should have a say in the public decisions that affect them. And the politics that matter most are the politics of anti-democratization against the politics of democratization, where anti-democratization seeks to restrict the people who have a say and the force of what they say to the benefit of incumbent-elites and where democratization is simply the struggle to enable ever more people to have ever more of a say in what affects them.
It has now become a commonplace for apologists for incumbent interests to respond to questions of public policy -- such as whether this dangerous practice should be regulated or whether that publicly useful infrastructure project should be funded -- by replying that we "should let the market decide" the matter. Such responses are predicated on ignorance -- more actively, on ignoring -- the fact that there is no such thing as "the market," really, that what passes for "the market" from epoch to epoch is an ever changing constellation of laws, norms, contingencies of geography and history, infrastructural affordances, and systems of signification. To an important extent "the market" derives from decisions we make, and to endow this result of our decisions with the power to make decisions for us, tends to amount to a relinquishment of decision to those who are already beneficiaries of the status quo naturalized as what passes for the moment as the dictates of "the market."
All of this is just to point out, that quite a lot of what we take for granted, treat as tidal forces supply and demand outside ourselves with which we struggle to cope and accommodate and exploit, are in fact public decisions that affect us about which democratic politics may demand we should have a say. When basic definitions of capitalism we find in elementary textbooks and basic dictionaries declare capitalism a system in which the means of production are privately owned and investments result from private decisions, the collective normative infrastructure on which such claims of ownership and the selective public allocation on which the legibility of such decisional authorities depend are disavowed.
Democratizing politics seek to secure equitable lawful recourse for the nonviolent adjudication of disputes (including disputes over what properly constitutes violence and equity and democracy); work to facilitate nonviolent transitions in authority through periodic elections, universal enfranchisement and office-holding and freedom of assembly and expression; have long struggled to provide a scene of informed, non-duressed consent to the terms of everyday commerce through the provision of generous welfare (universal basic income -- possibly via piecemeal provision of social security, long-term unemployment insurance, a living wage, public grants for IP commons, compensation for public exposure to environmental/medical risks -- healthcare -- possibly via piecemeal provision of veterans healthcare benefits, medicare, subsidized insurance, medicaid expansion, medicare for all -- education, civil rights) all paid for by progressive income, property, and transaction taxes, counter-cyclical deficit spending, and bond issues; and would eliminate the violation of common and public goods through their accountable administration in the service of commonwealth. The ongoing generational churn of the plurality of stakeholders who make up the present world ensures that the ongoing accomplishment of equity-in-diversity is endlessly renegotiated, re-enacted, re-figured. (For more on why taxes are not theft see this; for more on basic income see this; for another formulation of left versus right basics see this.)
All of these ideas have been implemented in comparatively democratic welfare states -- many of them have been implemented less well lately due to the influence of facile, falsifying capitalist and socialist ideologies, and most of them could be implemented incomparably better simply if the process and spirit of stakeholder compromise were to prevail (which you might say is another "mix" that isn't actually a mixture at all, but the substantial if interminable accomplishment of reconciliation of which the political actually, essentially, consists).
But while I have focused most of my disdain here on political systems that call themselves "capitalist" -- though there have been and are many quite importantly different capitalisms historically and presently, colonial, industrial, financial, and so on -- this is mostly just because my own country thinks of itself as such a system, and the crimes of perils of that system appall and implicate me in ways that demand response. But, once again, I do not think there is a pure "socialism" with which capitalism is being mixed and ameliorated in the better welfare states. The socialization of public and common goods facilitates their accountable administration and provides for a legible scene of consent to the terms of everyday commerce. The democratization of economic and ecologic life better describes what remains alive in the fraught history of socialist struggle and aspiration to me. Socialization is not an end in itself but a means to the end of Democratization. That socialism worth fighting for is democratic socialism, and it is its democracy that makes it so.