I'm only really for it if you could audibly tell "okay, this section starts here at this specific point & ends here", like in Octavarium, Six Degrees or A Change Of Seasons for example. TCOT flows too naturally for me to really consider it in sections, which I think is why it wasn't broken down. That & it has a fairly simple structure: opening-verse/chorus part-quiet part-epic climax. It doesn't really warrant any breaking down because it's doesn't really need it to be properly understood. Same goes for ANTR too: the way I see it is in verse chorus, & I see the Beautiful Agony section as the bridge, followed by an extended string of solos, then the final chorus. ItPoE is the same way: you have your opening, the lead-in to the main section, the verse-chorus, a faster bridge, an instrumental section, & an epic climax in the form of a final verse & chorus.
So basically, my stance is that you should only break it down if it's very glaring & very necessary, otherwise don't bother.