And isotopes. And transient, unstable configurations that may exist for a brief moment before decaying into something that slots into the periodic table better.
And also elements aren't a thing, quantum fields are. This is why you sometimes see things that just don't fit the idea of distinct atoms. But then quantum fields also aren't a thing. We don't know what exactly is the thing. We only have increasingly sophisticated working models.
No need to go to such philosophical depths. We're only poor engineers trying to come up with workable model. The periodical table of elements was a true boon and it is unlikely these "foreign keys" will change, but still - it alone isn't fully suitable as data model for chemistry.
And also elements aren't a thing, quantum fields are. This is why you sometimes see things that just don't fit the idea of distinct atoms. But then quantum fields also aren't a thing. We don't know what exactly is the thing. We only have increasingly sophisticated working models.