Ironically, I think you're letting your view of academia distort your own thinking here.
The mechanism isn't that complex. Anywhere resources are limited can lead to outcomes where an unequal society is worse off than an equal one. If I have a finite supply of doctors, for example, then the wealthy will be the ones who receive care while the poor go without.
The wealthy also tend to set up systematic barriers to ensure that the resources they fund serve them alone [1]. In the US, this is probably best exemplified by public education: schools are funded by property taxes, so rich districts have better schools, which in turn further increases home values (a process exacerbated by policies that prevent construction of cheaper, higher-density housing---policies supported by, naturally, the wealthy). Schools in poorer districts are therefore worse off than they would be if wealth weren't as concentrated.
Even if you take the perspective that, net, an equal amount of dollars is going toward education (or healthcare, etc.), it's fairly obvious the marginal benefits are different. A second violin teacher isn't as meaningful as adding a calculus class; elective cosmetic surgery isn't equivalent to treating diabetes.
[1]: https://www.theatlantic.com/magazine/archive/2018/06/the-bir...