I personally love pigeon pose, but it wasn't always this way. When I was just starting out practising yoga, I had the tightest hips, and sitting in pigeon pose (see below image) was almost impossible without toppling over to the side. I love teaching pigeon pose, especially in my Yin classes, but will never teach it without the use of some sort of prop. Here's why.
The traditional version of pigeon pose is lying down in a passive, unsupported forward fold over the front leg. We're often told by our teachers to "surrender", to "release into the hips", and to stay here for several breaths. Many teachers simply offer the use of a prop if you think you need it, but don't insist on it. This presents a few issues, in my opinion. A new student who is a complete beginner will not have a clue whether he/she needs a block or not, and will usually see this as a failure in terms of flexibility. The same goes for the semi-flexible, who will often skip the use of a block even though they could really do with being propped up more.
It's for this reason that I always ask students to grab their block and prop themselves up under their hip with it, or to fold up a blanket under the hips if they have a little more openness in the hip joint and don't need to propped up so high.
One of the main reasons for practising pigeon pose with props is that the very nature of the pose puts the knee joint in a pretty precarious position,with the added weight of the torso and upper body lying on top of the knee, which isn't beneficial for the knee or hip joint.
Many teachers guide students into pigeon with the front leg hip drawing as far over to the side of the mat, and the front heel dragging over towards the opposite side of the mat, in an attempt to get a right angle with the front hip. With this alignment, the student tries desperately to keep upright while keeping the front leg in line with the front of the mat, and try to bring their torsos into an upright position.
By propping students up with a block or blanket, students can find much more of a release in this pose, while keeping the integrity of the knee and hip joints safe.