Why should sustainable investments make sense?

So let's assume that there was an easy way to make a sustainable investment by investing into a great fond. So in this hypothetical fond only shares from truly great companies exist. Why should this make sense from a sustainability perspective? Unless the companies in that fond are selling their shares for the first time, the company won't ever see any benefit from me investing, will it? The invested money only gets passed to the person who held the shares before me. So I really don't understand why all the resources I could find stressed how great it is to invest sustainable and what a good impact one has. Am I missing something here? And, a bit offtopic, do you have an idea how to use the money so that it actually does some good?