Discord support is an annoying thing to use. live support will make your support system so easy. And everyone will feel comfortable using it.
Discord is a good channel for gamers and projects to communicate between team and community. For support, it is not good because not all users have Discord account and not all of them install their Discord on phones or computers. With Discord, you can use directly on web browser but you can use it on desktop application and mobile application. If not all users have it on their devices, support on Discord will be bad for them.
If you force your users to create a Discord account, install the app one their devices, you are create inconvenience for them.