Humans are already naturally choosing not to reproduce. We are seeing behavior in humans that is very similar to overcrowded rat populations. I don't think a total fallout will occur unless some very forceful manipulation is done to reproduction, whether it be for reducing it or growing it. I'll link you to that experiment, if you're interested. I have to dig around for it.
Here's my argument about monopolies: If a choice of various rail companies is truly desirable and the public is willing to pay for it, large investment will eventually occur to allow small and newer companies to compete.
To me the matter relies on the desires of the people and their will to achieve it. If it's something worth having, it will be done. If nobody willing to work for it or invest in a cause, why bother? Do people not know what's best for themselves? If you think the answer is no, then a parental government is usually the go-to answer.
The rat comparison only works on short time-scales. If you feed them enough, eventually they adapt and start reproducing again. The same goes for any living creature. The argument is very simple: if there exists any path for genes or memes to forge a group that reproduces endlessly, the first such group will exponentially take over the population until something stops it. Evolution has created proper fingernails and an abstractly re-configuring brain. It is certainly able to make people reproduce, and thus, this will happen until something stops it.
On the monopolies, your argument is correct. However, it works only qualitatively, namely if you assume a financial market of arbitrary size. Reality is not so nice. If a monopoly is so large that the biggest time-scale financial markets can cover is less than the expected amortization time, the investment never happens.
The good news is: your argument means there's no need for state intervention on small scales. The bad: if someone monopolizes something like operating systems or transportation on an entire continent, stepping in should be preferred to waiting for a miracle that might take ages to happen.
