It appears from your examples that “se” is optional, although I don’t see that explicitly stated. For example, “ Ayer me depilé las piernas.” doesn't have “se” in it.
Your example "ayer me depilé las piernas" does include the reflexive 'se' (since it's in the first person, it becomes me).
If we follow the logic of the lesson, these would be the two possibilities that could apply to your example:
Ayer me depilé las piernas. (Yesterday I got my legs waxed / Yesterday I waxed my legs.)
Ayer me depilaron las piernas. (Yesterday I got my legs waxed.)
In the first case, we can understand that either you or someone else waxed your legs and in the second example, it is absolutely clear that "they" did it for you, and not that you did it yourself. However, the most common construction is the reflexive one.
Finally, in your example "ayer me depilé las piernas", the pronoun 'me' cannot be omitted because if we do so, the benefit of the action of hair removal would no longer fall on the subject of the sentence, but on another person:
I hope this explanation is helpful.
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