The same reason that pills come in blister packs and bridges have nets-if you add a delay to methods for ending one's life, a significant portion of people change their minds.
One is to prevent unsupervised actions from taking place. This is usually to empower younger people to reconsider.
The other is supervised. This is usually to empower older to people to consider their options.
We can agree to disagree on what supervision means, but a bridge net and a mandatory process without a (subjective) additional waiting period, are very different situations to me.
Would you feel the same way if the waiting period were objective? Say a study was performed with varying wait periods, the percentage of people who changed their minds and opted out was tracked, and the final length was set somewhere on this curve to minimize both the delay and the number of people who may have changed their minds. There are ethical problems with that precise setup, but you get the idea.
The human psyche is a frail and changeable thing-a pause in a long-held mental routine can lead to greater consideration at any age, not just for the young.