Falling (with or without the slap) is only a small portion of ukemi. Talking about ukemi in just that aspect is like talking about one individual player while watching a football game. You're missing the bigger picture.
We learn to roll and fall for safety reasons, not ukemi reasons. We initially learn to slap while falling for safety reasons, not principle. That's an important aspect to remember.
Initially, while performing techniques, people have to have a vehicle for safe practice. Rolling and falling are that vehicle. It's a beginner's tactic until the student progresses enough to start understanding ukemi. All this slapping the mat is just a beginning learning procedure such that students can use energy and intent in an attack while also learning ukemi (not rolling and falling).
We learn to slap because it gets the body into a safer position when landing. It supposedly also distributes the force when landing. Again, this is a safety tactic so that a student doesn't end up landing on their head and/or neck.
Ukemi isn't rolling and falling. If you're at that point where you are rolling and/or falling, you've lost most of your ukemi and you're basically in the last ditch effort to save your body.
Ukemi is receiving energy and manipulating energy. Sort of like what Aikido is about. When someone is trying to do something to you and giving you energy, how you receive that energy is ukemi.
When you attack someone and they use Aikido, most of what's coming back at you is your own energy. What you do with it is ukemi. Good ukemi means you can keep your center and effect the other person. You'll hear this called reversing technique. Bad ukemi means you were fairly clueless about the resulting energy coming back and now you're in that situation where you have to roll or fall.
For example, when Dan did the no inch punch, my ukemi sucked. I couldn't receive the energy properly so my last resort was to fall backwards, which I did. There was no slapping. Just a nice, soft backwards fall onto the ground. The former was advanced ukemi which I failed and the latter was basic ukemi which I passed.
When talking about rolling and falling, well, IMO, most of the true ukemi has passed by that point. What one is doing now is merely receiving the ground in a safe manner. Nothing special about that. Most beginners can accomplish that in a relatively short amount of time.