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A system that expects all worthwhile things to be profitable will simply fail to do all worthwhile things and society will be worse for itI agree with the spirit of your message, but you're going way too far using all there. Some are not profitable, and the society is likely better off to socialize these. As a simple example: it's not profitable to provide food and housing for people without means, but if you don't, your society will be worse off - simply because these people will be forced into directions that are generally harmful to your living spaces.
Sure, you could increase police presence in this particular example, but that'd still be an effective socialization, because now you just put them on jail, which is even more costly then just providing them housing and food.