As a matter of anecdote, I've used some of this data for teaching purposes, and I've heard of others doing the same.
As Bryan notes, there is a list of journal articles that have used the data: https://openpsychometrics.org/_rawdata/cited/ This includes many well-regarded journals in personality and individual differences research.
One main limitation is that the data tends to be based around single scales. In contrast, I imagine in a lot of uses cases for potential publications rely on relating multiple scales with each other.
That said, I imagine these datasets could be useful for examining various general questions about scale properties and test structure. You could also look at demographic correlates of test scores. And the data would be interesting if you were interested in the psychometric properties of the specific tests that are reported.
A second limitation is that there seems to be limited information about the nature of data collection and data cleaning. That said, for many purposes, a massive online convenience sample of online participants may be useful.