Something can take effort to accomplish. No one would doubt that it took Einstein some great effort to develop his theory of relativity, even though it is an abstraction of a sort. Something can also take courage, take time, take honesty, take patience, take kindness, etc. In this case, taking means meeting a requirement.
However, the person actually expending this effort is making the effort. One can make an/the effort to be a better person, though this takes courage, honesty, etc. You can also make time to do things. Make is a complicated verb, one meaning meaning of which is to cause (something) to exist or come about; bring about. One makes changes.
edited to add OP's example:
It takes effort to become a better person.
People make an effort to be a better person...