I've heard it several ways, so I should ask here. In the case of a main chute failure, are the SuperDracos able to attempt a contingency propulsive splashdown to save Dragon's crew? If this is in the mission failure plan, what kind of envelope does this failure mode have? Can they use the SuperDraco landing option if multiple chutes fail? Can they recover from a tumble or spin after chute deployment? How low to the ground can the chutes fail and the crew still be saved (without excessive G loading)? Can they recover if the drogues fail and there is no main chute deployment at all?
Propulsive landing was the original plan for the Dragon 2, back when the Dragon 2 was also intended to maybe be used for Moon landings (Grey Dragon) and Mars landings (Red Dragon), where there is no or not enough atmosphere for parachutes. Plus, it would help commonize (is that a word?) knowledge between Falcon 9, Starship, and Dragon.
However, both of those roles are now being filled by Starship. Plus, NASA made it clear that the certification requirements for propulsive landing would be enormous, and they would probably still be required to carry backup parachutes anyway. So, parachutes it is.
Now, the question you are asking is: could they do it the other way round? Parachutes as main, propulsive as backup? And the answer is more or less the same: this would still require the propulsive landing system to be certified as a backup landing system.
It is simply much easier to spend the money, brainpower, resources, and effort, in making the parachute system more reliable than adding a completely different, separate landing system. They added a fourth parachute to the traditional three from the Apollo program, they used improved materials, they did a lot of testing.
Interestingly, both Dragon and Starliner, had quite a lot of trouble with their parachutes. It turns out that parachutes are a lot harder than we thought, and both stricter requirements from NASA as well as more comprehensive test campaigns from SpaceX and Boeing uncovered some serious flaws in the Apollo design that had not been known until now. This is why the development of the parachute systems took a lot longer and was a lot more complex and expensive than originally thought.
This might have been avoided by going with propulsive landing from the get-go. Or, we might have uncovered even more as-yet-unknown problems.
However that may be, at the time the decision was made, it was thought that parachutes were a well-understood, well-developed, safe choice, so propulsive landing was never seriously considered by NASA. SpaceX could, of course, develop propulsive landing regardless and use parachutes for NASA flights and Superdracos for non-NASA flights, but that makes no commercial sense.
Therefore, propulsive landing is out, and was never developed, and is thus not available, not even as a backup.
You also might ask yourself: couldn't we at least use them to "cushion" the landing like the Soyuz does by firing them just a few feet off the water? This has some additional problems. First, I believe the thrust is so high that there wouldn't actually be much difference between hitting the water and hitting the "brakes".
But more importantly, handling of the Superdracos is currently rather simple. They are safed after reaching orbit and then never turned on again. This means that there is no possible way in which they could accidentally fire in the vicinity of the ISS, for example, or during recovery operations. Otherwise, all of that would have to be certified, too. (The ISS guys are understandably very peculiar about what can be fired with how much thrust in which direction while in the vicinity of their station.)
As to your hypothetical question raised in the comments, there is an additional wrinkle. At the moment, the Superdracos have enough propellant for a Launch Escape. They share their propellant with the Dracos, which are used for Orbital Maneuvering, but the beauty of that is: when you fire the LES, you are not going to orbit, and when you are in orbit, you no longer need the LES!
This is, however, not true when you use the Superdracos for propulsive landing. Then, you must carry enough propellant for Launch Escape and landing – there's not much point in escaping a fireball on the pad, and then die from impact on the water. So, you would need more propellant for a propulsive landing, which may or may not weigh more than the parachute system.
One last possibility for using the Superdracos would be the re-entry burn. This currently takes 11 minutes with the Dracos, whereas it would only take 5s with the Superdracos. However, that is exactly the reason why it is not done: if the burn takes 11 minutes, then being off by a tenth of a second is only an error of ~0.01%, whereas with the Superdracos, it would be an error of ~2%. Therefore, the lower thrust gives more accuracy.