To start out; I want to split gold sinks into two types: necessary and luxury. Obviously being a game you could argue that all are luxury. Let's pretend that some things are necessary: repairs, class and profession training, mounts (one of each type) and training, reputation gear, and the AH cuts. Pets, extra mounts, and toys (except the train wrecker) are luxuries. As such, they should not be considered when attempting to balance the economy. Is epic flying a luxury? I will say yes. But if not, then it should be considered a part of the leveling process and should therefore be paid for through quests and vendoring while leveling.
For all of this, take note that I am only talking about farming which adds gold. Mining will help you get gold, but it isn't adding gold to the economy unless you're vendoring it, which you probably are not. All gold is coming from NPCs, since those are the supply of gold to the economy. Quests, dailies (I am separating these from one-time quests), vendoring, and coin drops are the inputs of gold.
When leveling was slow we were usually able to loot enough, vendor enough, and get enough from quest rewards to afford training and repairs. Sometimes we were a bit reckless and died too much or were slow to get bags and had less to vendor, but overall we got gold as we needed it.
Professions are harder to train. Vendoring the crafted results will keep up with training, barely. Of course I just broke my "farming isn't gold supply" claim, since leveling professions are an exception; leveling in general follows different rules than end-game. Enchanting gets screwed up since the greens they'd vendor instead become dusts which cannot be vendored. They could trade enchants for greens to balance their own books, but overall enchanting reduces the gold input to an economy.
Ideally the economy would be balanced for each section of levels; that players in their 30s might benefit from trading with others in their 30s, but no one needs gold from 80s or 60s. Level 30 should support level 30 activity. This isn't the case, as Gevlon points out.
Let us pretend for a moment that leveling is balanced, perfectly balanced. In this hypothetical scenario, a player will reach 80, finish training all their professions, talk to their class trainer a last time, repair their gear, hop on their flying mount, and now they have exactly zero gold. Leveling is self-contained and we can now ignore it and focus entirely on the creation, circulation, and destruction of gold at 80.
Let's go back to our level 80 gold sinks: repairs, reputation gear, and the AH cuts. Repairs can be handled with a few dailies, in the current system. What if we didn't have dailies? What is the rate at which one can pick up coin and vendor trash from purely grinding mobs? If that rate is sufficiently quick to cover repairs without requiring endless grinding, then repairs do not require dailies.
Reputation gear is a one-time cost. It is logical that the gold needed to buy the reputation gear should be acquired in the process of grinding the reputation. If it is a grind based on dailies, then they should give enough for a player to buy the gear from that rep (and no more). If it is based on mob kills, the average kill count should give enough as well. Wearing a tabard and running instances is about the same as mob kills and can be combined into the average.
If mob kills can cover repairs, then that leaves only AH cuts and deposits as the last end-game gold sink. Dailies actually make these worse. An unlimited source of gold promotes careless spending, which means higher prices, which increases the rate of gold loss, making it appear as if dailies are needed. In fact all that happens is they promote inflation, encouraging further grinding to keep up, and continuing the inflation even further. Dailies make us poorer!
I do actually like the idea of daily quests. They can be a more interesting alternative to mob grinding, and that's a good thing. But they give such a high amount of gold that they overcompensate for the gold shortage and just make things worse.
If you needed dailies to afford flying, don't take that as proof that dailies are broken, but that leveling is. If flying is a necessity, then it should be covered while leveling. Only luxuries and repeating costs (repairs and AH) should have to be specifically farmed for.