This is a good idea, but it would cause a large amount of issues in the process. The question is, do the cons outweigh the pros?
If you created a character in Alpha, which had Alpha Weapons, you bought Founder, you had the Beta Gear and Gamma Gear, and you traded that to a new account, without any of the achievements etc. this would create a lot of confusion, since large amounts of players have these weapons without achievements. This may be solved by restricting these items, so that they cannot be transferred over.
Furthermore, if you decided to make a new account and traded over loads of rares to it, then people would be incredibly confused as to why there are level 1's running around with rare weapons. Again, restrictions may help this, by only allowing weapons around your new char's level to be transferred.
You buy Weapons and other items on one single character. If you can freely transfer them from one to another, then you'd only have to buy all the items once. This means that there would be a lot of people on new accounts who have fully enhanced weapons, and have an advantage over others, who are having to earn their items from scratch. This theoretically could be the same idea as a 'universal inventory' where all your characters use a single inventory, and you can use all your weapons on each, since you'd be able to do that anyway while transferring your weapons to whoever needs them, then you log out, transfer it back to your main, and battle there. Feel 'oh, I feel like battling on this account', transfer it to that one. It makes it so you don't have to earn the items more than once, which would be a huge balance issue between those who have played through before, and those who are new and playing from scratch.
As you can see, there are a lot of things that go against the suggestions, it's a great idea, but on a whole, I just feel that there are more cons, than pros. While it could be great, there would be a large amount of restrictions on it, it would take a long time to code, and in the end, have a system which would confuse players and balance.