Perhaps the Valar felt that it was time a Dwarf was allowed in since the Elves, Men, and even Hobbits had seen the Blessed Lands. Given how much effort the Dwarfs had put into fighting Morgoth and his servants it might have seemed just to allow in one, particularly one so involved in the fight against Sauron. As well as the other reasons given in the quote above.
I wonder what Gimli's time there was like for him and how long he was given.
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