The narrative that socialism is incompatible with capitalism
That one's actually true. You're likely making the common mistake of thinking markets/free trade and saying capitalism.
While markets and trade are necessary for capitalism to exist, the opposite isn't the case.
Capitalism is an economic ideology where accumulation of capital is the ultimate goal and highest virtue.
Socialism is an economic ideology where the ultimate goal and highest virtue is for wealth to be distributed in such a way as to create the most social good for everyone, especially those that need it the most. That's by definition incompatible with capitalism. Its entire POINT is in fact to replace capitalism.
- The narrative that the free market can regulate society fairly, rather than always leading to monopolies
Yeah, no such thing as a completely "free market" is possible.
An unregulated market will inevitably encroach of the freedom of those with the least wealth and power, and regulating it is by definition making those with the MOST wealth and power less free to oppress the rest, for example via monopolization as you point out.