You don't get it, absolutely
First, I'm not saying that all coins created equal is communism. This was only to show you how false your approach is. Further, you don't understand what the word utilitarian means in this context. In the given context it means serving for achieving particular end, so if something doesn't help in reaching it (or even gets in the way), it is either non-utilitarian or even anti-utilitarian (for this specific purpose). This is not about free market versus communism dichotomy at all. It is about whether something is utilitarian or more (less) utilitarian for a given purpose. Miners as such play only utilitarian function (whether you like it or not), that of confirming transactions (and generating new coins). The whole thing is certainly not about them earning profits, it is not the purpose of mining. Beyond that purpose they are useless. If you proceed with this understanding, you will likely see my point
Profit is the incentive to fulfill their purpose, or utility. You surely recognize this
I couldn't make out what you meant to say, apart from this part
Indeed, profits are the incentive for miners to do their jobs, up to a certain point. But there are a few things which I mentioned but you seem to have failed to notice. First, there is no reason to think that this is the only way to create a decentralized payment system (otherwise known as blockchain), so there is no reason to think either that those who are confirming transactions should (and would) do that for profits only (thus your whole point of communism versus free market becomes irrelevant). And, second, this idea (profit as an incentive to fulfill the purpose) ultimately gets severely in the way of fulfilling that very purpose since miners start to care for profits (in the form of fees) more than for making their job (i.e. confirming transactions)