Of course, the Grail can be traced back to the chalice used by pagans to represent the womb of Mother Earth, containing underground water sources, the amniotic fluid, the life giving beginning of all life.
The fish, which represented Christ, the vesica pisces, originating in the triquetra of the Triple Goddess before the Triple God. If we take the chalice and water as symbols of female fertility, the fish and the rod (and also the spear of Longinus) the male aspects, biologically, of fertility and the changing of the Maiden into the Mother aspect. Full of belly. The Fisher King, needs the water of life from the chalice of the goddess, to heal from his injuries, become a healthy man again, a king able to cater for/to and look after his queen and provide (for) a family, filling her belly with food and with children - again, as you said, fertility rites again, even though the Christian God had a curiously sexless way of procreating, even he (we are told) needed a woman's belly to swell to produce a son and heir! Older fertility rites such as those which happen at Beltane, transfer us into a more fertile time of the year, exchanging a Winter (Holly) King for a Summer (Oak) King - often represented by stags, the old replaced by the younger more fertile who then spreads hus seed to produce new members of the herd. It's all ultimately about Nature and Life. And the stories that were told throughout time to explain that which was as of yet scientifically understood.
(Sorry for the ramble, not well today, but you got my juices flowing, so to speak, lol)