I don't have the issue with this that many seem to. I would consider applying a limit to the number of instances a student can do this, and I would keep the original class and grade intact on the transcript. But adjusting the overall GPA to reflect the better of the grades is a relatively minor GPA adjustment in the long run of 130 credits, I think.
I wonder how they came to the idea that it was needed? Did they do some real analysis to see what the impact would be? The additional tuition aspect aside (ulterior motives for the school), will it keep more kids in school who might otherwise drop out due to frustration and self-doubt?
This could help a qualified kid get an initial job they might otherwise be passed over for.
From my pov, I like the fact that a student persevered and re-took a class to get a better grade. We could all use a few mulligans in life! Young people grow and learn at different rates. Some 18-20 year olds need a wake-up call. I'm more interested in where they are than exactly how they got to this point. And I'm more interested in where they are headed. Correcting a mistake is a positive sign of growth.
When hiring, I want smart, motivated, positive people, and my experience says they usually succeed in the job and the in their career. I was a B student in college who took a couple of classes over due to Fs. (Yes, I was even more immature and clueless than I am now.) I knew a number of guys in my fraternity who were smart and seemed to put schoolwork way down on their list of priorities, yet who became huge successes in their fields... company Prezes, CEOs, PhDs, starting their own companies.... They took advantage of the mulligans they were given.
How people react and recover from their own screw-ups and young adult immaturity is more important in gauging probable success than an adjusted GPA of 3.1 vs. a raw 2.9 GPA, imo. And aside from the first job or so, who really prioritizes a person's GPA when considering their qualifications once their career gets going?