do they not realize the elements of harmony could banish Celestia to the sun, right? And can't she undo the ropes with magic, same goes for Trixie, and any other unicorn in Equestria? Wouldn't pinkiemana diane pie destroy Celestia? Rainbow Dash no break pole or Celestia's face with sonic rainboom speeds? Applejack breaks pole with an applebuck or Fluttershy sends a bear to maul Celestia and cut the ropes? Why would they burn her on a wooden platform!? So little sense is made.... I LIKE IT.
Well, I think the sun of Equestria is actually an artificial star, that they need as a satellite, in order to make their world (in)habitable, probably because their world is too far away from the actual sun of their planetary system.
Also, Celestia might need to perform a rejuvenation ritual, to give the sun a life-extension, by reverting the age of it, similar to how Saint Walker made his first task as the very first Blue Lantern, by using the Blue Light of Hope to postpone the fate of his home world's solar system.
if i can point out one thing this seems to be a bit out of character for Celestia. it seems like she is normally depicted as being very reasonable and understanding. maby this could be her fear of what could happen to her?