I don't think being phone-only is the key there. Telegram is not phone-only and I'd say it's as easy to use as WhatsApp. In fact, for non-technical people it essentially behaves as a blue WhatsApp and I've heard it described exactly like that, but if you want to go beyond that, the functionality is there. This kind of software that can accommodate several "levels" of users is sadly becoming rarer and rarer.
Discord is IMO quite a mess. I am definitely a technical user (also lived in IRC for years, that's why I'm on this thread) and as someone who just uses Discord from time to time, I regularly get confused by it and find a nontrivial amount of friction to get things done there. No wonder your parents struggle with it.
Not convinced - I certainly don't find Discord any more complex or harder to use than Telegram. The main problem my parents had was they kept losing their account details and creating new accounts, and I think any system that isn't phone-only will have that problem (yes you can make accounts unique by email address, but my parents have multiple email addresses that they mix up, so that doesn't solve the problem). Disabling web browser use and making it harder to sign up (or harder to use without signing up, or locking down server invites even more strictly) would "help" a bit, but I like having a chat system that people can try out in the browser before they commit to it.
Discord is IMO quite a mess. I am definitely a technical user (also lived in IRC for years, that's why I'm on this thread) and as someone who just uses Discord from time to time, I regularly get confused by it and find a nontrivial amount of friction to get things done there. No wonder your parents struggle with it.