What is the purpose of using a transparent proxy?

I don’t get it.

Apparently they can be used by companies to create whitelists and blacklists for employees.

A transparent proxy is useful, for example, when you have guests or employees connecting to your network, and you need to control their activity.
They connect through the transparent proxy, and you have your transparent proxy server managing some aspect of that activity, for example, filtering out certain sites, asking them for some kind of proxy-auth, etc...

I suppose not every site or app will check X-Forwarded-For headers and such, so they could be used in certain situations with the same anonymity that a normal proxy will give.