But! But but but!
Sam DOES follow, just not right away. Sam lives a long, prosperous, ridiculously happy life in Hobbiton with Rosie, with whom he has many children. He was mayor of Hobbiton SEVEN times until he retired at age 96, oversaw the establishment of the Shire as its own independent land, and was personally given the Star of the Dunedain by King Elessar as a gesture of friendship and love. But when Rosie passed away on Mid-Year’s day, Sam rode out from Bag End on September 22nd for the last time and finally followed Frodo to Valinor as the third and last Ringbearer to do so at the grand old age of 104.
He did exactly as Frodo asked him to. He was whole, and happy, and he enjoyed and did more than he could have ever imagined when he was a humble gardener listening in for tales of the Elves. And when he had lived out his life in peace and absolute happiness he earned his reward and followed Frodo home.