One additional issue with propulsive lsnding is that you need legs, and they need to penetrate the heat shield. This significantly complicates and weakens an absolutely critical part.
Not sure that's true. The chutes bring the speed of the capsule down quite a bit, just a short burst of the dracos at the last few feet could allow it to softly land and wouldn't require much propellant. This is exactly what the Soyuz does. My guess is that this approach was rejected by NASA (not SpaceX) due to complexity rather than feasibility.
If the engines don't start, or you don't get the predicted thrust out of them, well, that's why it's called a suicide burn.
Fair enough, but this is exactly what the Soyuz has done for decades, and NASA (as well as Roscosmos) found the approach to be acceptable for human spaceflight. It may introduce complications, but it's clear that it's doable.