Mondragon's example goes exactly against all of your points. It's a 70k workers company ran as a co-op. You can have co-ops running and trading between them, the only point where capital is necessary is for investments in new businesses lines (in the sense of financing capital, not all capital, financing capital from banks can also come from co-op banks).

Undesirable jobs are done either way if people are paid, there's no difference if it's run by capitalists, the government or a co-op, you need to hire people and pay them. A co-op would work the same way.

Capitalism is definitely not like Democracy, democracy has been proven since ancient Greece to be a decent system to organise power, and it has evolved over time to be more inclusive. Capitalism has only shown that if left untamed and to grow on its own it will only consume more, exploit more, and remove freedoms of being a human being in the world if you don't pay up.

Capitalism is useful but every decade it seems to be reaching the limits of what it can be, no better version of capitalism has emerged, every evolution of capitalism has only magnified its destructive power. Democracy has done the exact opposite.