Most Matrix bridges to commercial chat systems also require accounts on those networks. That's the only way to make them work on most of these systems.
I guess you are specifically referring to the Matrix to Discord bridge that does work like you describe, but a similar bridge has existed for XMPP to Discord in the past but is currently broken and unmaintained. The currently working XMPP to Discord transport does require you to puppeteer a personal Discord account, but that is rather because of a different focus of the used transport framework than any technical limitation of XMPP in that regard.