Sadly there is no option like "it could use support of other professions for some of crafts" :P
I don't mind BS relying on Alchemy for some crafts (it is cool idea to have professions to interact with each other in some way), but atm BS is completely not viable without Alchemy at all. Every craft, even weapon chain and belt buckle, requires Alchemy's daily cd (! not just some alchemy craft, but daily cd).
Mining is the real culprit here, I don't know why you choose to focus on Alchemy. According to WoWhead there are over 600 Blacksmith recipes. Less than 10% of them require mats that come from Alchemy. However a full on 90%+ of those recipes needs mats that come from miners! If you want Blacksmithing to be self-reliant then I would say start with 90%+ and petition that it be untied from mining. If you disagree with that then I think you should petition for disenchanting and cloth gathering to become seperate professions so enchanters and tailors are in the same boat.
The reason i focus on Alchemy is due to the Living Steel.
Tailors can make Imperial Silk either once per day on a 24 hour cooldown or they can use Song of Harmony to get their higher tier items themselves more often hence negating the 24 hour cooldown if they have the mats.
As a Blacksmith we have to mine the Ore and Trillium from what i've manged to get is hard to find and also has a 50 / 50 chance of being White or Black. But even once we have the ore turned it into bars we can't do anything with it.
It has to go to an Alchemist.
Tailors can make their high end mats and craft their own items, Same for Leather workers.
Both of those professions should you choose to follow them to make your own armor are self reliant.
Blacksmithing is not.
Now there are several ways that this could be reworked but the fact is people will always disagree.
I just want the general populace's thoughts on it.