Chrono Trigger (Activation of)
Several stipulations surrounded the Chrono Trigger's activation. These were spelled out by Belthasar and Gaspar; specifically, they noted that the Time Egg would have an effect equal to the amount of effort given toward the achievement of its intended purpose; that if it were being used to save a person from death, that the person in question must be important to the space-time continuum; that a clone would be needed to satisfy the second requirement, and that it would have to be used at Death Peak. Why?
The short answer? A lot of this spiritual talk wasn't in the original game. For the first two stipulations, the Gurus were probably intending to encourage and instill confidence in Crono's friends to steer them toward reviving him, a task that required much effort (as Death Peak was difficult to climb and sported Lavos spawns that had to be defeated).
GrayLensman, Ian Chamberlin
Concerning the clone, it was placed there so that Lavos would not know Crono survived the incident after he was saved. This would give the time travelers' an edge and keep Lavos from knowing beforehand that he would soon fight the time travelers at the final battle. Also, seeing Crono disappear might have alerted the party, Schala, and Queen Zeal as well.
Pocket Dimension Aperture
Death Peak is where Lavos erupted in 1999 A.D., meaning he exited his Pocket Dimension there. This means it might be easier to access the Pocket Dimension there than anywhere else. Considering that Crono died while facing Lavos in the PD, this move is logical.
From: Theory (Objects)