As a DM, there are two reasons I ask this kind of question.

If it's a player that I know is comfortable playing their role, then I am trying to get them to lean into the scene to assist with story pacing, or potentially to reveal additional information.

There are still benefits to asking it though, even if a player is not comfortable playing out the scene. Even without a spotlighted stage, you can still obtain a lot of character development by asking for additional clarity. For instance, did the character want to use a cheesy pickup line, or maybe a humorous anecdote, maybe they want to be really suave.

I would probably ask some leading questions like the above, but that additional info can still greatly expand the scene without turning it into a night at the improv.