What are "higher quality cops"? People with more developed morals and ethics? Money does not necessarily attract more compassionate or kind people. There are plenty of other high paying industries where that's not the case (e.g. banks, real estate).
I think the idea is that low pay actively excludes many high-achiever types who are capable of making much more money in the private sector--without gambling their lives. You cannot recruit the best and brightest unless you can pay a competitive salary.
Paying more doesn't guarantee 'higher quality' but it sure helps.
That is a very unusual speculation. Do lower paid people have less compassion? Do high school teachers have worse understanding and appreciation of ethics and morality than bankers?