Anyway, back on topic, I do still think that trying to distinguish between great albums and perfect albums (as Ed articulates) is an odd exercise. The perfect is a subset of the great.
It's an interesting point and perhaps part of the discussion that Ed was trying to induce and as you specifically used one of my own album choices in your first post (namely Gomez's 'Bring It On') I feel I ought to wade in.
For me, the distinction between an album being one of your all-time favourites, simply by being one you love listening to (which sadly clearly the Spice Girls example you gave would fall into for some people!) and being 'perfect' lies for me largely in the combination between the technical merit aspects of the album and the level of enjoyment I get from listening to it, but there are many more factors besides.
In the spirit of Ed's title, in my original post I did try and explore some of the factors that made my choices perfect for me. But others may use their own criteria. On the subject of commonality though, this is perhaps the area that some could be reached.
The final choices will always be different though because of the differences in personal taste.
The idea of technical perfection versus enjoyment in music is an interesting one though, highlighted by some notable tracks and albums that have been created in recent years using AI (essentially just an output from computer algorithms). Technically perfect? Maybe. But do they reach into your soul the way music really ought to? Actually, I've heard a couple of really good examples, but that is still another question entirely and one that surely has to be part of the criteria for being a perfect album, but which maintains the subjective element. Thus why commonality can never be found.
In that regard, no-one has managed to work out what it is about music that makes it enjoyable, other than the fact that particular types of music for particular people affects a particular part of the brain causing a dopamine rush (much as drugs, sex and food do) and while there will always be certain examples that manage to excite that response more widely, there will probably never be a single album that manages the feat for absolutely everyone. And certainly not while maintaining technical brilliance, artistry, individuality and any of the other factors which for me make an album great.
Ed's question asked for 'your' perfect albums, which to me inherently incorporated personal preference and subjectivity.
But as to the question of 'the' perfect album, well surely that doesn't exist.
Some great choices on here though and a great way to listen to some albums I've never heard before, enhanced by the fact that they are, at least in one person's eyes, 'perfect', which makes the whole exercise more than worthwhile.