Privacy is a huge concern. It's difficult to phrase this properly without sounding like an asshole, but Discord's development team has a lot of very young people (no proof, but I'd swear some of them are 13-16 years old). If you've ever listened in on their Discord voice channels, the level of immaturity is astounding. Power to them - it's great to see talented youth create a great product. I just wouldn't trust them with a business's confidential information.
Discord's specifics aside, it blows my mind that people use any off-site SAAS for internal communications, including Slack. The database set contains so much critical information, including infrastructure passwords, private SSL and SSH certs, etc. Employees will send anything and everything over the company's chat client. Even if you trust the company's employees and general security, the fact remains that your uploaded attachments typically have a public URL not requiring authentication to download.
End-to-end encryption is essentially useless/unsolved when it comes to large, dynamic groups like Slack channels. Any new member who joined wouldn't be able to see any history in any channel.
But this is not a problem of Discord but of all group chats. The initial discussion point was that Discord might be insecure because of young hackers building the product.
I would gladly pay them.