The issue isn't so much that people who donated for SM aren't willing to complete the SM chain on their own for the Sealed Chest items, but that it becomes much more inconvenient for them to do so after already having acquired SM. A lot of guilds won't give Shadowfrost Shards to someone who already has a SM equipped while there's someone else in the raid who's on the quest that doesn't have SM and thus has a more tangibly legitimate need for the Shadowfrost Shards. It's completely understandable and fair that a guild would distribute Shards this way, but part of what it does is it works against people who bought it years ago back when buying it or having it as a lucky drop were the only ways of possessing a Shadowmourne. A lot of those people donated for SM then not because they just wanted to quickly exchange some cash for an orange item without having to go through the bother of a several months long quest chain, but because it was simply the only way to acquire it back then.
I don't know how feasible the following idea would be to implement, but I think it rather elegantly solves the problem of old SM donors not being allowed to acquire Shadowfrost Shards by raids and guilds, whilst also making it so donating SM doesn't automatically get you a Sealed Chest. Basically, it would work very similiarly to how Transmog scroll "drops" work atm:
If you're a Shadowmourne wielder, but you're also at the stage of your quest where you have to collect 50 shadowfrost shards and you defeat an ICC boss in 25man mode, the server rolls a 25% (50% on heroic) chance for you to automatically have a Shadowfrost Shard added in your inventory (or by mail if your bags are full - standard stuff), and this Shadowfrost Shard that gets rolled whether or not to spawn for you works exactly like a Transmog scroll in that it isn't acquired from the boss' loot table per se, but is still a random drop nonetheless that just gets added straight to your bags. Basically, the boss would still drop Shadowfrost Shards as per usual which could be looted by anyone else on the quest, but a restriction should probably be in place where SM users can't receive them the actual way from the loot table, but can only have them as random spawns in their bags.
This makes it so people who pay for SM but also want a Sealed Chest still have to go through the entirety of the quest chain, but do so without being held back from their quest progression on account of already being a Shadowmourne possessor.