I have this feeling that they have almost as many sysadmins and programmers with the same amount of budget, but more of their profit is getting greedily absorbed by their shareholders. Because why bother spending more money on infrastructure and customer support when you can just pocket all of that fat cash?
As far as I know, reddit's never really been that profitable, and in fact has been operating at a loss for several years... see this article from 2013 as an example. Also, it's a private company, so in order to have shareholders to be beholden to profit-wise they'd have to go public first, which also means that they'd have to have proof that they can be profitable... which is quite likely why Pao was brought in. That said, they do have a board of directors, but it's pretty much just Alexis Ohanian and maybe one other dude.