First, do you consider "the majority" a good metric by which to measure an economy's success? Simply "more than half" able to provide for themselves? I don't, personally. I think as a society, we should strive for 100% of people to have access to food, water, shelter, medical care, etc.
In terms of the current capitalistic economy in the US, yes, I do. And it's not more than half able to provide for themselves in the U.S., it's more than half of adults living in a middle-income households. this means that much more than half have at least modest amount of disposable income.
It's a laudable, albeit impractical, goal to strive for 100% of people to have access to all of these aforementioned things, with no caveats. The sheer strain that would be placed on these systems would deal more damage than it would fix. Even if everyone was able to pursue their preferred careers, I doubt that we would see any real increase in the quality of the treatment in medical fields (I'd argue there'd be a severe decline), and the fields would most likely still suffer from being overburdened. Housing issues are also more nuanced than they seem, with the logistics of allocation, construction, and regulation of housing being a nightmare in multiple ways. Most people in the US already have access to food and water, but even so, droughts still have a wide-ranging effects, especially in the west, and stretching such a system further thin would be ill-advised. Food and water still mostly remain a non-issue in a theoretical situation where they are distributed evenly, at least in the US, and are more simple and practical to deal with than the other issues. In other countries they would remain a severe (and perhaps the most important) issue, however.
Second, and this is coming from a US-centric position since that's where I am and that's what I know best, the USDA estimates that one in six househoulds are food-insecure - that is, they do not have access at all times to sufficient food to feed their family. Again, this does not meet my criteria for an acceptable system. Is it the worst? Of course not, but to say that workers are "not stripped of at least a reasonably livelihood" is incorrect.
The statistics that you provide invalidate what you're saying. I say that,
...the worker is generally not simultaneously stripped of at least a reasonable livelihood. I'd wager that the majority are at least able to provide for themselves, at a base level, with some disposable income left over.
So a majority of workers can be said to not be stripped of a reasonable livelihood if they have enough food for themselves at all times, and I'm assuming generally some disposable income. 87.3 percent of U.S. households were food secure throughout the year in 2015, with a declining trend from 14.9 percent of households classified as insecure in 2011 compared to 2015's 12.7 percent. The USDA says,