I think the big things that prevent it from being adopted more for professional use is the lack of a threading model (even though I hate it when people use threads in Slack) and the whole everyone in every channel except for role-based privacy settings. The second one especially is a big deal because you can't do things like team-only channels without a prohibitive amount of overhead.
That said (with zero knowledge of their architecture) I have to feel like both of those missing features aren't too terribly hard to build. Its very likely Discord is growing as a business fast enough on the gaming and community spaces they don't feel the added overhead of expanding into enterprise (read: support, SLAs, SOC, etc) makes sense and are waiting until they need a boost to play that card.