A transaction fee of what? To take a fee from a transaction there has to be a transaction to take a fee from, which needs some sort of "coin" that came from somewhere. Somebody has to create a money supply and distribute it somehow. When the network first comes into existence, nobody has any money, so where does it come into being from?

Mining is what generates the coins. And you need mining because otherwise you need some other issuing organism. Without decentralized mining you get a central issuer, and that's untrustworthy and possible to shut down.

It is subtle, but PoW mining itself doesn't generate coins. It isn't like someone is digging a hole in the ground and extracting gold.

PoW miners are rewarded for correctly validating transactions, with newly minted coins.

The whole proof of work thing is that you proved that you validated a transaction by expending energy, and the network pays you for that security service.

Miners then need to sell those coins on the open market in order to pay for their capex/opex, which creates the market.

The open question is that if you have a fixed supply of coins that eventually runs out, what will carry the miners?

It'll be increased fees or the network will switch to another solution.