That is an interesting argument, but where is the proof? Economics is a very murky “science” as it is, a broad statement such as “capitalism is inherently unstable” needs some healthy data backing it up.
Marx makes his case for it in Capital, specifically Volume 3, Chapter 13-15, though it’s easier to digest Wage Labor and Capital and Value, Price and Profit. Essentially, competition forces prices lower, and automation and increased production lower the price floor. Automation is pursued because it temporarily allows you to outcompete, until other firms can produce at the same price, forcing prices to match at a new floor. This continues. It’s more like gravity than an invisible hand, there do exist ways to push back against it, but the overall trend is negative, as the Rate of Profit falls to 0.
The same argument could be made about communism, as an economic system it doesn’t have the best track record.
It can’t, because Communism abolishes this system. Communism has a good track record when properly put into historical context and is definitely the correct goal to pursue.
Socialism seems to have a pretty good track record. But even in socialism there are issues, especially around ensuring a steady supply of kids coming through, once population starts falling the cracks start appearing.
Socialism is just the precursor to Communism. The USSR, Cuba, PRC, Vietnam, Laos, etc. are/were all Socialist, building towards Communism, I don’t see why you say Communism has a bad track record but Socialism has a good track record, that seems contradictory. Further still, I don’t see what birth rates have to do with anything.