Why would the fee-charging miners go out of business? Wouldn't the fee-charging and non-fee-charging miners just coexist? If one large miner decides to confirm no-fee transactions instead of fee transactions, this will not economically incentivize the rest of the miners in any way, as far as I know.
This is spot on. The speculation of such an occurrence has very little foundation within a free market.
Contrary to what you said about this not happening in a free market, it is indeed the ability of people to choose freely whether or not to pay a tx fee which drives the tx fee charging miners out of business. Likewise any miner is totally free to choose whether to charge fee or not.
I will try to explain better my earlier response to this question you quoted. Keep in mind this is after the block rewards dry up. The compensation for mining is only the tx fees.
Say half the miners (or even more) refuse to include in blocks they mine the transactions without a fee. The other miners will process all tx regardless. People are therefore incented to not include a tx fee, because statistically their tx will eventually be processed by miners who don't require a fee.
The people who don't mind waiting a few blocks for their tx to show up won't pay the fee. This loss of revenue will make it unaffordable for some miners on slimmer margins to mine, and they will drop out, which causes the relative network hashing share of the fee waiving miners to grow. This causes the wait time for blocks including transactions without fees to be shorter. This further incents more people to not include a fee. This makes profit margins for fee charging miners even smaller, and drives out of business more miners who need that fee. This causes the relative network hash rate of miners who don't care about fees to grow again, which statistically means blocks containing tx without fees will be found even sooner. This makes it so even more people don't include a fee. This causes..... yada yada yada yada yada