Note that Thiel is describing the inevitable goal of capitalists, because in the long run of perfect competition, all profits tend to zero. Technology and innovation are certainly one way of ensuring that the ceteris do not remain paribus.
However, Thiel is not recommending monopoly as a policy for society. Only the most ardent libertarians argue for pure laissez-faire anything-goes capitalism that results in lazy extractive rent-seeking monopolies.
The best balance for society seems to be free markets, which are as free as possible, but no freer.
A free market needs rules against: monopoly and oligopoly; price gouging but also dumping below cost; predatory acquisitions that concentrate markets; monopsony in the supply chain and the labor force; collusion, corruption and insider trading.
It also probably requires positive requirements for truth in advertising, verifiable product standards, open data, published product specs (like food contents), health & safety in the workplace, and protection of the commons, in the form of environmental rules against dumping toxic waste and pollution of air, water and soil.
Free markets also need low barriers to entry, which are in tension with some of these protections. The guide should be as free as possible to allow competition. Many regulatory measures, such as professional licensing, put up barriers to entry that enable rent-seeking behavior for those behind the credentials & licensing walls. Obviously brain surgeons and nuclear power plants need some regulation, but perhaps real estate agents or hairdressers do not. The requirement for open data should make both brain surgeons and nuclear power plants publish their track record.
There may also need to be long-term strategic regulation for the climate. Again, it is best to leverage the power of free markets to achieve that goal. Some form of carbon/methane hydrocarbon tax seems worthwhile, as it will create incentives for new businesses and technologies. Also note that the free market will take care of other effects naturally: we will see falls in property prices for the eventually-to-be-inundated suburbs of Shanghai and condos of Miami (hint - don't park in the basement :)
It is counter-productive to tax things that are desirable, like income and employment, when what should be taxed are undesirable activities, like greenhouse gas emissions. So tax carbon, maybe keep some of the vice taxes on alcohol and drugs, but remove all income and payroll taxes. The Gulf states tax oil production and do not have income taxes. Let us tax oil consumption and also not have no income taxes.
I would go as far as to say, only tax carbon if all income taxes are removed.
