Presumably, a Reddit leak means even more opportunity to unmask (dox) users who have responded truthfully to threads that say things like "what's the worst thing you ever did". Lots of blackmail opportunities.
All outbound clicks from the site are redirected via out.reddit.com which ties click activity to an individual (username / IP / device fingerprint based). This can only be blocked with aggressive old.reddit script blocking which breaks portions of the site.
The outbound click data is used for profiling and interest based advertising, but the data can be much worse than simply linking comments to identity.
They also tie IP/identity to individuals to serve relevant ads and this is the push to get people installing reddit on phones, where deviceIDs is an easy UUID for ads.
Having a disconnected online entity means less-than-pleasant jackasses can't pull something from years or even decades ago, put it out of context, and proceed to troll your life.
Not putting your real life identity on public display for the world to see means you maintain tighter control over how, when, and where your information gets out. Do you really need your real name, face, place of employment, telephone number, email address (with your name in it), and maybe even your home address publicized? More than likely you don't.
Having online identities disconnected from real life means you can use them to safeguard your actually really-fucking-important real life things. Your bank account? Use an email that uses a nickname instead of your real name so any would be hackers have to second guess your email too.
Worst comes to shove and shit hits the fan, you can throw away an online identity and make another one. You can't throw away your real name and face.
There are nothing but benefits by keeping your online and real life identities separate, and if you ask me it's one of the first steps to being truly internet literate.