I'd dispute the statement that good grades are a useful measurement of ability to function in society. All grades really measure is students' abilities to get good grades. There are lots of factors that can go into getting a good grade, especially in courses where the grading process is necessarily subjective: writing in a style which appeals to the grader, building a relationship with the grader, studying in an optimal way for taking exams, being dedicated to your studies, etc.
Parts of this skillset are obviously useful in general. A person who is able to figure out how to appeal to their audience will do well in many fields. Some are more tricky; for instance, one might assume that someone who studies optimally for their exams will be able to figure how to perform other tasks optimally as well, but this is often not the case. One particularly misleading thing about grades is that they are often seen as an indicator of how dedicated/good of a worker students are. This might sometimes be the case; some students get good grades primarily because they work very hard. But some students get good grades without much effort, some only work hard because they have someone driving them (such as their parents), and some do well in an academic atmosphere but will burn out in a more job-oriented one. The biggest of these fallacies is that a student with low grades is a poor worker or bad in their subject; there are students who worked hard but just had a bad teacher, students who are overworked, students who prioritize certain classes over others, and students who are disenchanted with academic work but who will do well in a "real-world" atmosphere".
As an anecdote: I go to a fairly alternative liberal arts school that is nonetheless highly ranked (not that rankings are good judges of schools, but here's the US News page: http://colleges.usnews.rankingsandreviews.com/college/items/... ). My school accepts a fair number of students who in high school did not perform well academically. Many of these students pick up their grades while here; nearly all of these students are very smart and capable.
The problem with grades is that they fail to provide any breakdown of the factors which contribute to them, which is the truly useful information. Even in the cases where a student got all A+'s or all F's, where it seems that the student is probably overall competent or incompetent respectively, there are still external motivations which are not taken into account but which are nonetheless vitally important.
Another big problem with grades is that they fail to take into account differences between environments, school policies, and graders; that is, even when grading policies are objective, they differ from place to place but are compared nonetheless. Different graders grade differently; some may give A's to everyone who is qualified, while some may give them to only those who are most qualified. Some of these effects can be damped through normalization, but usefully normalizing grades seems difficult as well. Imagine trying to normalize grades between MIT and community college students. Additionally, the information required to do any significant statistical tricks is often not avaliable to those who could use it, and those who could use it would probably not take the time to even if they could.
Finally, I feel like you completely missed the professor's point. (I'm assuming he believes arguments similar to mine.) Since grades don't provide signifcant metrics of anything, using them to judge people is both discriminatory and a bad idea. Thus, the responsible thing to do would be to get rid of them altogether (or at least reform them so that they actually measured something). But since he doesn't have the power to do that, he does the closest thing he can: give everyone the best grade possible. This has several positive effects: it lessens the potential future discrimination against his students; it, as you said, "compromis[es] that whole system", making more obvious how arbitrary it is and hopefully leads to its undoing; and it (he believes) makes students learn better.
He hasn't ignored the second task at all.