IME, I try to nail the notes at the precise pitch in relation to the piano (or guitar) when playing pizz, especially on a ballad. No vibrato ... like the low strings of an in-tune piano. There's always a time and place for vibrato, but I hear my first obligation as providing the precise pitch for all of the other instruments to get in tune with. Vibrato can make the intonation a little wonky, especially in the low register. There might be many exceptions of course!
Here's an example of a ballad with the WDR Big Band on "My Romance" arranged by Dave Horler. The intro is unison bass trombone, piano and bass—vibrato wouldn't really help that passage. I want to match the pitches with the bass trombone and piano exactly, without any fuzziness around the core of the pitch. I don't really use any vibrato, as you can see at the little ensemble section snippet at 1:16 and at 1:29. When I play a solo beginning at 5:10, then I'm using vibrato on some of the notes. When I go back into time for the trumpet solo at about 6:15 then I’m not using vibrato. That's how I hear it