Apologies for this digression away from the main topic of D major chords.
2020 may also be an F#dim (triad, i.e., F#mb5), but that doesn't stop it from being a D7 as well, even if a "rootless" one. We play many rootless (and thirdless and fifthless) chords on the ukulele—the main forms we use for 9th chords, for instance, are all rootless (there are alternatives, but they drop out some other component). It is a myth that a chord must include all components in its theoretical form in order for it to "truly be" a chord of a given name.
In fact diminished triads are used infrequently, far less frequently than 7th chords, and usually in contexts where they function harmonically as rootless 7th chords (which is how our brains tend to interpret them). It's rare that adding the missing 7th root would not fit (i.e. when the chord would definitely be an F#mb5 rather than a D7 harmonically). There's also the issue that if, in a lead sheet, you were to spell the chord as F#mb5 instead of D7, you would be artificially limiting how a player would render that chord (2020 is far from the only choice)—as well as obscuring how the chord fits into the harmonic structure. I consider both consequences bad things. mb5 chords also tend to be more awkward forms to play than either 7th, dim7 or m7b5 (half-diminished) chords, which usually serve better with more "fullness". I can think of only one song I play in which I definitely want a mb5, and even in that song, upon the third occurrence in a single line I substitute a m7b5 to develop the harmony and improve the voice leading.
