Let me make you a counterproposal - why don't you offer the winner of a roll the vendor value for the item on the spot? Basically you'd do the same thing you do with the shard - your party allows you to roll need on any item nobody else wants, and you pay the winner of a roll whatever vendor value for the item is. After all, he won the item, and all he can do is vendor it anyway - now he isn't out any money, and although you don't get the mats for free, they're cheaper than the AH price. Once you've bought the item, you can disenchant it and nobody would argue that you deserve the shard.
As for the ores and the leathers, almost all of them can be and are obtained outside the instances as well. The few exceptions really need to be discussed in the party before the run begins - things like the Pristine Hide of the Beast, the Souldarite from Hakkari veins, and so forth. But in most cases, these are done by guilds, and either the guild is getting the materials or the guild miner/skinner is expected to share his mats with the rest of the guild. Same with enchanting on guild runs - in those, the enchanter usually keeps the mats but is expected to provide important enchants for guild members.
I was in a Scholo run with a gentleman who wanted Dark Runes for crafting and had a very creative solution - he didn't mind rolling greed against anyone for the rune, but anyone who passed on the rune would roll for 1G. Those of us who had no real use for the rune except to sell on the AH were more than happy to have a 1 in 5 chance at 1G on the spot and let someone else have his crafting mats.
And as for people not collecting the shards for their own enchants, you're dead wrong on that one. Almost none of the enchanters I know provide mats for their enchants, especially the ones that use shards, unless they are just desperate to level their skill. If I want an enchant, I buy the shards at the AH for whatever the enchanters think they're worth, then tip the enchanter handsomely for waving his wand over my item. An enchanter on the run who will disenchant a soulbound item that I win for me is a generous soul - one who feels he should be allowed to roll need on every item that drops because he really needs the mats to level his enchanting is a ninja.