Market, employment at will, and other such things could be saved provided that those who lost the rat race have a sufficient safety net. i.e. welfare. Where lack of psychopaths would help is, for example, the unwillingness(or diminished willingness) of the leadership to create externalities(e.g. pollute), game the rules, lobby lawmakers for laws that give unfair advantage, generally behave unethically towards competitors or consumers. And for people who are supposed to regulate all of this the prime sin is selling out.

Some systemic changes to capitalism are needed of course: abolition of corporations(only private companies, with real responsibility for decision makers and owners), and (100% minus capped_inheritance)(let's say $1 mil) estate tax, are the most obvious ones, imho. And it would be easier to adopt them without psychopaths.