The Consequences of the Events at Mount Doom

[Diamond18]

I don't think it was just one particular thing that made it neccessary for him to go to the Havens. Merry was also wounded by a Ringwraith

But Merry did not have to go to Valinor as a result. He became prosperous, popular, happy, got married, had little hobbits, and in general enjoyed the Shire in every way that Frodo didn't.

So the fact that the three hobbits who go to Valinor are the three who were Ringbearers is most telling.