I think conflating capitalism with trade is wrong. Trade (and markets) existed long before modern capitalism. So did the concept of money.

I agree that the way you described it, it sounds very natural (not that that really is an argument, but whatever).
But the reality of capitalism is that the Y I’m buying from my profits is not some other commodity (as your example implies).
Y is someone else’s business that also sells X. Or some completely unrelated business that sells Z. Or Y is a bribe to the mayor so that the city buys all its X from me, even though I don’t have the best quality or price. Or it’s a “donation” to the new mayor’s campaign, leading him to remove the rule that one person can not own more than 3 homes in the city, so I can buy more houses and rent them out and make more profit.
It’s capital I use to open X businesses in other cities. Maybe someone already sells X there and the local citizens quite like their service. They don’t care for my X. But I have enough capital to start aggressively underselling, at a loss to myself. Now it doesn’t matter that my service is worse, or that the people had some loyalty to the local X seller. I’m selling at half the price, it’s a no-brainer to buy from me. I wait a few months and the local X seller is now out of business. I can raise my prices back up, nice. This works quite well, I’ll repeat it in other cities. If someone catches on and complains, I’ll just bribe the mayor to look the other way. Or I’ll buy the local newspaper and have them paint me in a positive light.

I agree that blindly throwing money at a problem is not a good solution. Unfortunately this basic insight is often abused into an argument that spending on social programs shouldn’t be increased at all, or worse should be decreased.
Well targeted social spending is actually profitable for the government. Healthy, housed, educated citizens produce a lot of value.