The debate really is no brain. It is like the kind of debate between new-classical economists and new Keynesian economists, the truth is always some where in between.
Keynesian realise that market can have problems from time to time in getting full employment not soon enough and that is true, so government has to do something to aim at achieving full employment.
Even that theory works, then there is politics that endangers the theoretical fiscal policies that will be needed to ensure full employment.
Then, there are further problems with markets, it is not just aggregate demand or supply that are the only issues, there are structural and inter-temporary issues that are not too dissimilar to the aggregate issues. Those kind of structural and inter-temporary issues also need policies to manage and government is needed to play that role to address those issues.
Then of course income allocation has been recognised as an issue so government constantly work on taxation and welfare policies.
All those issues added together, you have a much bigger role for government to play in the economy: that is essentially some kind of capitalism and state work together, or some kind of state capitalism.
Of course, countries may differ in the kind of issues and their severity that requires different kind of combination of market and state, akin to the kind of Samuelson’s synthesis of classical and Keynesian economics.