I certainly haven't perceived the multiple 'deaths' as a flaw, though my dreamy optimism is well known to more than a few Downers.
Like Firefoot, I happily accepted the emotional roller coaster of concern set up by the characters' apparent demises and joyous recoveries.
In Frodo's case, the repeated brushes with death seem to set up the necessity of his journey into the West. That final trip acts as a symbolic death by sending him to a far-removed land from which there is no return. Each of Frodo's encounters - the Morgul-blade, Shelob's sting, and the tableau following the Ring's destruction - injure him deeply and irrevocably. If taken with his last journey out of Middle-earth, perhaps Frodo's close calls truly are deaths on some level. The ending of the part of his psyche that would have allowed him to recover and live in the Shire as the other returning adventurers did.
I can certainly see Eowyn as having a 'death' and rebirth. The Eowyn who went to war is different from the one who fell in love with Faramir. Following her near death in battle, she has learned that she doesn't need to be a queen or seek glory as a shieldmaiden. The change is more dramatic than I would have expected to come from mere recovery from illness, as if she needed to go to the brink of dying and then return to gain a new perspective on life over her next days in the Houses of Healing. I'm unsure, however, on the relative importance given her experience in battle versus the effects of being healed by Aragorn. This requires further investigation from me when I have access to my books...
Merry and Pippin both return to the Shire as different Hobbits than when they left, though my impression is more of experience gained through adventure than a rebirth. Something else to recheck.
So my opinion is that the motif does play a role in the development of the story, rather than being due to chance (or lack of other plot-twists
)