You have to, because people do not work for free ("each to the best of their ability, and taking according to their need") if they can freeload. The only way to get them to be productive members of society is either a carrot (the capitalist system, which offers an improved standard of life for those who work hard), or a stick (the communist system, which offers imprisonment or death if you do not work hard). That force is political in nature. You cannot have a communist system without it also being a dictatorship.

So I'd say that having a capitalist system is a requirement for also being a democracy. Moreover, the rapid fall of the fascist nations suggests that having a capitalist system is, in fact, also conducive to not having a dictatorship: economic freedom leads to people wanting political freedom as well.

The problem with capitalism is that people misunderstand it to mean that some billionaire owns 'everything' - whereas it really is YOUR freedom to choose how YOU lead your life. I'm all in favor of curbing predatory practices, but all too often 'taxing the rich' turns out to mean 'taxing the middle class'. The drive towards ever-heavier taxation, where tax rates only ever go up, and never down again, can only be fought by striving for more capitalism.

What does the theory of capitalism have to say about people who do the work but never get the carrot?

No True Scotsman in 3, 2...

It says they either chose that option for themselves and are happy with the outcome, or that they will find the outcome unsatisfactory and move on to do something else, something with more carrots.

I'm not sure why this is even a question, you could have thought of this yourself: "I think I'm not earning enough. Should I stick around in this job or find a better one?"

Your snide comment is also not a response to what I posted, but I guess presenting a counter argument is just too difficult.