Staccato exercises are good for the voice. They access quick, rhythmic and spontaneous movements. They allow the voice to reset itself between pitches. They can help the ear-mind-throat connection to become more nimble. They are usually best learned in arpeggiated patterns, but can also be done in scalar patterns.
After the student can sing an arpeggio both staccato and legato, it can be interesting to explore the degrees of articulation between staccato and legato. Bowed string and wind instrument players spend years working on gradations of articulation from the driest staccato to the most connected legato. Singers can do that too, with good results.
I have found it helpful to construct exercises where the space between staccato notes is gradually shortened, but the staccato impulse still begins each note. When the notes are all connected but still being approached with a slight pulse on each one, I explore with the student the various ways that we can get from one pitch to another in a legato phrase.
Note transitions can be completely slurred as in a glissando or “scoop”, or in several other ways, with less or more staccato function in the transition from one pitch to the next. Working with the staccato function can give us more choices in singing intervals. Experimenting with the staccato movement within the context of a legato phrase can lead to greater subtlety in phrasing. It can help with the execution of difficult leaps, allowing the upper note to find its balance in a freer manner. It can prevent the tendency to “overthink” or “mess with” a note, since a staccato note lives for such a short time. This can lead to a better understanding of how the attack of a note is the most important part of how the rest of the note sounds.