Happy Holidays to you, Rowan.
Not to get too bogged down in detail, I think Marx was correct that capitalism would generate successive ‘crises’ and that eventually one would occur from which capitalism could not recover.
As far as I am concerned, that happened. We call it the Great Depression. Capitalism did not of itself recover from that economic catastrophe; deficit spending by government (to fund WWII) ended it.
Capitalism has been on life-support ever since. Constantly increasing debt, public and private (which increases the money supply and/or, it could be said, money’s ‘velocity’), has obviated the intrinsic falling rate of profit that Marx saw as capitalism’s Achilles heel.
As far as private property goes, I didn’t realize there was any great debate about that. I am personally ambivalent about people owning land, but I don’t see how abolishing ownership of land could be an economic panacea.
‘Real’ capital (land, buildings, machinery) was the functional key to the economy in the emerging capitalist economy of Marx’s day; money is the functional key to the contemporary Modern economy [capitalism + (proactive) government + (a proactive) central-bank monetary system].
Politically, changing the way money is supplied for the economy should be a much easier task than abolishing private property would be. It would provide the means to eliminate unemployment and poverty — without costing anyone anything or taking anything from anyone — as well as taxes and public debt. It could be accomplished through a single legislative Act, even without any changes to the existing institutional structure (if implemented through the central bank). As I said, the democratically distributed income (the means of supplying the economy with money — along with the funding of government) could be extended to eliminate exploitation.
A Marxist should not overlook the change in the structure of power that this paradigm engenders. It would be most evident in minimum-pay positions, where employers would be using benefits to compete for employees, rather than people competing for available jobs.