Is this activity across all the servers you're a member of or is it a social Discord? Just my personal experience, but there isn't too much chatter on product-focused Discord servers so it's easier to get to every message. I also have a totally separate Discord account that I use and make sure every message to the server ends up as a push notification to my phone.
If its that slow then you might as well just run a mailing list instead. More of your current and potential users know and understand email than discord.
I can confidently say our users would be 100x less likely to sign up for a mailing list.
From a user perspective, Discord is much better than email. When you give out your email, it's basically giving an entity carte blanche to spam you. With Discord, the user is more in control of when and how they interact with your community.