I've been pushed for time and unable to give your comments the attention they deserve, but I have a couple of things to say.
I don't think there is (or can ever be) an all-encompassing reason for using the sestina form or for repeating end words in the manner the form requires. OK, I don't like the workshop metaphor much, but it's popular and recognisable so I'll use it. I think of poetic forms as another tool in the poet's toolkit, tools that may some day come in handy, or may sit up on the shelf untouched. Or it may be that I take one down sometimes, check the moving parts are well-oiled, maybe make something interesting with it, maybe not, but take comfort from the fact of knowing it's there.
Many examples of sestinas have been posted on this thread, and in each of them the author probably had (in their mind at least!) reasons for using the form as a means of bringing that poem into being. I've written several, most of which have started out as something else but somehow asked to be written that way. Sometimes the motives are conscious, other times it is only after looking back at the poem (often after a period of time has passed) that I might understand why the poem needed to be that way. And of course there are those that never reveal themselves . . .
I should probably stick my neck out here and show a couple of my own, which some of you may remember.
This one was written with my mother in mind and didn't start out as a sestina.
Some people who read the poem commented that the form complemented the woman's repeated actions and slow struggle through the days that her son was at war. I hadn't intended that, but I like the idea!
Here's another. Again, it didn't start out as formal, but I did quickly get an idea of what I wanted to do.
Poem for Noam
Several authors have used the form to evoke a feeling of obsessive or neurotic behaviour (Bob's Sestina is a prime example!) and I wanted to tap into that idea with this poem.
On a general note regarding workshops, my basic approach is this: Fuck it, why not! I write every day, have probably written over 5000 poems, less than 5% of which are probably any good; and only about a third of those I would consider submitting for publication. Most of what I do is just playing around, exercising the muscles and making sure I'm ready for the muse when he/she turns up. You might think that's crap. Fair enough. I've attended dozens of workshops and lectures where I have decided within minutes I disliked or disagreed with the speaker/tutor. But my attitude always stays the same: Fuck it, why not!
EDIT: Err, OK, I just realised I misunderstood your question Ian and you weren't asking WHY people write sestinas but WHY they rate them . . . oops! Well, I hope my rambling kind of answers your question from my viewpoint anyway . . .