The info isn't needed for the conclusion advanced. Just one will do to "break the mould"--the point the speaker apparently wanted to make. Maybe not your point, but the speaker's allowed to have a goal different from yours or mine.
English semantics aren't always logical, but Grice hit the main themes in the 1950s a bit before I was born. Among other "maxims" or ways of talking he included "give all the relevant information" and "don't give too much information". These were good for at least 70 years before and after he published them for educated American English.
To indicate "34 felony convictions" is too much information and ventures into speech act uncooperation. Since we assume you're not being intentionally rude, we readers would assume that other presidents had been sworn in with felony convictions, maybe 1 or maybe 33, but not exactly 34. In other words, the communicative goal is to stay that Trump was the first with specifically 34. The specificity must serve some useful function besides pretension or assertion of superiority, right? But being the first felon is surely more important than being the first felon with ***34*** convictions. That's the main point and it's a worthy one. It may exclude information not important to the point, but that's not to deny it.
Saying he was the first with a felony conviction does not entail that he had one and exactly one felony conviction. Notice, "a" is demoted in importance. Speaker could have said "with one felony conviction." Where's the focus, what's important? "Felony conviction." Which is really, IMO, the most important bit of information. Want additional, add it in later.
I'll defend the speaker's native intuitions, understanding of educated American English discourse principles, and communicative competence.
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