Seven days is the plan for people who want to remember the trip rather than complete it. Each city gets two nights, so every sight has room, and none of the days is built around a long drive plus a long list.
The additional night in Agra is what changes the trip most. You can see the Taj Mahal at dawn, return for breakfast, and spend the afternoon at the quieter places: Itimad-ud-Daulah, Mehtab Bagh, and the old bazaars. Photographers in particular tend to love this version.
With a full day each in Delhi and Jaipur as well, the route moves steadily, and has room for an optional village visit or a stepwell on the road to Jaipur if the mood takes you.