The case for the album to be classed as a masterpiece can never deliver the definitive answer that is going to align with everyone's opinion and that's what makes discussions like this so cool.
Opinion is key to how you see the album, but looking back at it thirty years after the event seems to have removed the clarity of how the songs stood up against what had gone before and those which were of the time.
It seems that its difficult for some people to differentiate between being over familiar with songs and actually thinking that they are average. (Streets, along with Pride probably suffer from this more than any other songs). It's long been the case that the unreleased U2 song is always seen as better than the released version when, in fact, it's just different and hasn't been listened to death. Even Mofo, a song that is seen as being the best on the excellent Pop, has suffered from this in recent times and the alternative has never been heard in full!!
The Joshua Tree also suffers from the same problems as the band in general do: it is deemed cool to vocalise dislike for the sole reason of elevating their own "eclectic" and "more interesting than yours" preference.
The lack of metrics makes it difficult for anyone to be wrong or right. So we're only left with opinions. My own is that TJT is a masterpiece. My reasoning is this. U2 at their very best can be considered as good as any other band that has existed. They are more than capable of producing a masterpiece when performing at the top of their game. The Joshua Tree is U2 performing at the top of their game.
As good as TUF was, TJT is at another level, one that very few bands have ever reached. It was the soundtrack of 1987 the world over and has been held as the inspiration for other bands and musicians to exist. The quality of the best tracks is unquestionable, lesser ones more so. As a whole, the album is cohesive, inventive, thought provoking and paints scenery in a way no album should be able to. All qualities we would wish for the next album to possess.
It is so good, that U2 themselves were only able to better it once (AB) in terms of those qualities.
Although I prefer the high points of Pop and Passengers, I can't deny that those records would have been improved if the consistency matched TJT.
So, if there is such a thing as a masterpiece, then why shouldn't one of the best band's that ever existed be allowed to have one of their very best albums put in that bracket.
Yeah we can make a case for at least one other U2 album to be considered as a masterpiece, but that shouldn't take away the brilliance of this offering. As the saying goes, lighting other candles doesn't take the shine away from your own.