Sorry for the late reply, been stuck to just a phone as of late heh.
Anyways, there is a key difference you overlook in your timer comparison (while a good one), in that the timer encompasses all actions and is a mandatory part of the game. Lcanceling only exists for one action out of hundreds: landing during an aerial attack, and even then missing one is not always a penalty based on both enemy (in)action or the move simply either spacing the foe too far to punish/koing outright. The timer dictates all actions, and running over it will either always result in a penalty or even straight loss.
A smallish, but important distinction.
Going back to actions for a moment, while it does happen often, I do find it sort of odd that only landing an aerial has an added cancel input. Why not extend it to grabs so that you always have to jump cancel a grab for it to be fast (20 frames normal, 10 jc'd let's say). This would accomplish the same feat as Lcancel does currently, for a different action, and even has some of the same weakness in that screwing up leads to either slower action or unintended input (jump vs shield/dodge). Most however would not be happy with such a change, but why?
Let's look at the one actual bit of depth Lcancel can provide: it gives a way for players to mess up and be punished. Oddly, the depth really comes from the human element of when you *don't* Lcancel. Given it is a near required input to do fast offense, no matter how good you are you will mess up the added input eventually, and your mistake could give momentum to your foe. Lcanceling allows you to, in a sense, avoid mistakes as it makes your options safer. However, what does this mean for those who don't or at least rarely mess up an Lcancel? At that point, it may as well be auto if the execution is no longer a barrier to them, and the depth of making a mistake in a missed cancel shrinks phenominally if not disappears.
Back to the grab, people wouldn't like that because it'd add yet another area where they could make a mistake and thus be worse, just like Lcanceling. People who master it may as well not even know the punishment of failing it exists while simply providing a buffer of time to those not at that level for no real reason other than dedication it seems.
To sum up, Lcanceling adds depth in that it provides a means to swing momentum in rare circumstances when the player messes up, but only on a specific action in a certain scenario. Without it, gameplay may have less punishes from aerial assaults, but how often did this occur vs those who never/rarely messed up anyways?