Agreed. As always, it depends on what the author is trying to convey. At the first meeting, you probably do want to describe the walk in a way that reveals the character's inner motivation. Are they excited to walk up to the woman? Scared? Bored? They would walk differently depending on the feeling.

But a different scene might be better with the pedestrian "walk". Imagine that the main character enters the woman's office with an ostentatious bouquet of flowers. In that scene, maybe the emphasis is on the flowers or on the reaction of the woman or her co-workers. In the scene, a simple "he walked" might work best.