Why did Dasharatha not follow Ram into his 14 year exile?

Valmiki Ramayana mentions that Dashratha desired to go to the forest with Rama. He wanted to take all the royal resources with him, as conveyed in his desire to make “the forest into Ayodhya and Ayodhya into the forest” with the forest-like Ayodhya left for Kaikeyi to enjoy.

But Kaikeyi opposed him rabidly, saying that when he had promised her the kingdom, it meant the kingdom with its resources. She accused both Dashratha and Rama of underhandedly going back on their word.

Rama was pained to see her accuse his venerable father and so decided to honour Dashratha’s word by departing for the forest immediately. Dashrath hoped fervently till the last moment that he could somehow avoid Rama’s exile, by requesting him to stay for at least one more day during which he would offer his beloved son all royal luxuries.

But Rama, not wanting to prolong the agony of the unavoidable bereavement, started to leave immediately. He asked the minister of Ayodhya, Sumantra, who was his charioteer to drive him swiftly. Despairing Dashrath ran after the chariot, calling Sumantra to slow and stop. Seeing Sumantra slowing, Rama told him not to prolong the agony. And as the chariot speeded, Dashrath trying to catch up fell to the ground and watched in dismay as the chariot became a speck in the horizon and then disappeared.

His anguished courtiers raised him and took him to his room for rest. Dashrath never came out of that room, because he passed away during his sleep that night.