Actually you might be right. Although I think the ring would be the primary reason his ass is called to Valinor. Considering Sam too eventually had to go
Discussion
nostr:npub1jacntdqvalt27vngj9hwhjyqzppeayq7hnm2xmf7747t84yz32as4czppv nostr:npub1w4jud2zhl9ztd5pycpzsq9nf07c3vcguavtrc6jypvtd6qealy9sl8cead nostr:npub106dam65ww9ztdqj26xvh08dyuc7lj7nmkrtrujwsmyq2n6g3r33saq3m89 They didn't have to go but it was a gift to them as ring-bearers I believe. Frodo was very faded because of how long he held it and because of his wound, so he in particular would've suffered endlessly if he didn't leave Middle-Earth. Bilbo was quite faded as well as he hints at when he says the famous butter over bread line.
"‘Alas! there are some wounds that cannot be wholly cured’, said Gandalf — not in Middle-earth. Frodo was sent or allowed to pass over Sea to heal him — if that could be done, before he died. He would have eventually to ‘pass away’: no mortal could, or can, abide for ever on earth, or within Time. So he went both to a purgatory and to a reward, for a while: a period of reflection and peace and a gaining of a truer understanding of his position in littleness and in greatness, spent still in Time amid the natural beauty of ‘Arda Unmarred’, the Earth unspoiled by evil."