Your quoted me on the fourth page, man.
Not necessarily. The author has left plenty of bread crumbs, and some times, he expects the reader to be knowledgeable enough to connect the dots. 'Tears of Blood' is straight out of Orthodox religious mythos, where the sinners thrown in hell persistently cry out of abject and eternal misery. The grief is so profound, that they spend their tears and blood starts trickling out of the tear ducts. There is also an idiom for that, that 'you will cry tears of blood if you don't stop what you are doing.' The idiom has direct relation to suffering and spending ones allotted tears in hell.
This quite smoothly transitions into suffering that is a prerequisite for MS unlocking and it's accompanied by 'Tears of blood' every single time. In fact, when Obito inadvertently uses Kamui he even states, "am I in hell?" Furthermore, the eye also continues to seal itself. That is nothing but more added misery, as the Clan that prides itself on its eyes has to sacrifice its light and continue on persistently and slowly towards the inevitable darkness - another metaphor for hell.
Combine all this with the 'literal' summoning of Black Flames from Hell accompanied by the Tears of Blood metaphor, and what you get, is an extended Metaphor: meaning, the theme of suffering and macabre romance is repeated within Uchiha Clan dynamics over and over again via the unwilling quest towards darkness, the bloody tears, the references - subtle or otherwise - towards hell, and the relentless quest towards light.
The 'curse' is a metaphorical term, because the clan cannot progress in ranks without knowing extreme suffering - a theme synonymous with hell. They have to look for light in the discarded eyes after their own MSs fail them. All the while endeavouring to quell the building factors of darkness within the clan in regards to poisonous foresight in form of Izanagi, and curbing on that arrogance through Izanami. You cannot simply consider the terms 'curse' and 'tears of blood' and 'sharingan' separately. All of them are linked to one another, and the motif is further complicated because the names are plucked out of Japanese Mythology as well.
Just imagine how much of human psychology is explored here. Quite a lot, and quite intricately. Amaterasu journeyed to hell. How many Uchihas face this hell - the motif references - on regular basis? Their eyes were double edged swords. At one hand, they have the unmatched power of foresight, and on the other, the same sight becomes a matter of a Limbo like factor for them, when in order to progress forward, their journey towards hell is inevitable. Again, don't take hell literally here, as even the hell in Mythologies has sparked a lot of debate in regards to human psyche and the darker sides of consciousness.
Coming to the rest of your post, because mine goes too far into the literary dissection category, what you are going for doesn't have anything to do with Depth. Note that, that the term 'Depth' is independent of circumstances within writing or the plausible plot points that lead up to it; it's associated with the clan itself. Sealing Tech is not an extended metaphor. Definitely not in terms of characterization and that's what I was referring to.
Sure, there is not a shadow of a doubt that your points on increasing the clan's importance via their background is most valid. But what will it add to their Depth as a clan? Would it really make any difference if they sealed things? What impact would that have on their group dynamics that would take on the shape of varied metaphors that might end up defining the individuals within the clan themselves?
Nagato's past is more dynamic because of what happened in Ame, and the political skirmishes. Sasuke - or any Uchiha - and Sharingan, and Uchiha cannot be separated from the political factors and the workings of their own Clan's emblem, the Sharingan. Here is why I stated that Uchiha Clan has that depth, that recurring elements of several Motifs that take on the shape of underlying allegories. You cannot say that for any single clan, not even a single one.
The depth is attained from several of these themes working side by side with Sharingan and the clan dynamics, and the politics. Can you really state for a fact that any clan even remotely matches this level of Depth and Plot Intricacy? There is a reason why Kishimoto doesn't devalue the Uchiha clan and Chose Sasuke as the plot Catalyst and the central character - because his clan and his background allows for it. It's too rich, with many layers of figurative factors shouldering it.
Can you really say that for Uzumaki clan? I don't think you can.