The context is important, it was written in 1927 after millions dead in USSR and Mussollini has just won in Italy.
The same page:
"...Repression by brute force is always a confession of the inability to make use of the better weapons of the intellect—better because they alone give promise of final success. This is the fundamental error from which Fascism suffers and which will ultimately cause its downfall. The victory of Fascism in a number of countries is only an episode in the long series of struggles over the problem of property. The next episode will be the victory of Communism..." - Von Mises
https://mises.org/library/liberalism-classical-tradition/html/p/29
I'm well aware of the context. We know from history exactly what the allowances of these men whose only concern was property were prepared to tolerate; it was indeed, as you say, an appeal against the specter of communism and the fear of the propertied against losing their power that led to the Nazi destruction of Europe. To Von Mises fascism was an inconvenient necessity in the face of communism; to fascism's, and thus capitalism's, victims, irrelevant.
This seems to worry that the fundamental concern is that even if there was wealth being produced such that every worker could live a very rich life (and casually subsidize non-workers), we'd still need to push for communism because the system itself would be unstable? Or maybe that the communism would happen regardless after the system destabilized? It's a worry about future suffering? Or is a worry about the current outcome of the (hypothetical) system?
Some people talked about continued concern about the disparity between wages, but that doesn't fully make intuitive sense to me, since my major concern with capital floating to the top is that it's becoming increasingly difficult to earn a living wage. Or, in other words, there's a problem with the current system delivering the essentials. Being able to overwhelmingly deliver the essentials would mollify this. I'd gladly let the hyper-rich exist if the income of the worker was rising sustainably (especially if there was some type of causal link). With that as the target, all I really care about is the rate at which it's growing.
They go hand in hand: that is to say, the aggregation of capital you identify as a problem is at its root the most fundamental economic critique of capitalism, that it is unsustainable because capital aggregates in such a way so as to make the markets dysfunctional. The fact of exploitation is a sidecar to that: there could be no capitalist exploitation if capital couldn't aggregate. There may be other forms of exploitation, but it wouldn't be capitalist exploitation vis-a-vis private profit. Any Plenty that markets could provide is eliminated by the beggaring of those markets to big capital: whenever the capitalists get richer, the workers' share of the industrial output drops, and they naturally, by market mechanisms, become unable to afford as much of the industrial output that they could afford before. In my view this aggregation and this beggaring of the workers is a natural capitalist process.
This is why this concern or anxiety you identify is there: if it is indeed the tendency of capital to accumulate, then what must be done to prevent it from accumulating or, indeed, reverse that? There is a good deal of reason to be pessimistic about the capitalist accumulators having any interest in voluntarily ceding the power they've worked so hard to gain, so we're forced to ask what options are available to everyone else to, say, avert climate disaster and make the capitalist accumulators accountable to the society they've profited from and the environment they've destroyed.
A hypothetical society that eliminated capital accumulation must necessarily be socialist in my view. Even if the mechanisms are a sophisticated mix of market and planned economics, if capital cannot accumulate so as to make people unequal, then that is not capitalism.