Only reason for it is not implemented, because it would require operation to transfer data between 2 databases, which is not as easy as sending things to your char in same realm
Any idea how much money Blizzard make from server transfers? At £15 per character, a lot.
Any idea how many people put heirlooms onto a mule just to pay to transfer that mule to a new server because they're sick of their own? A lot.
Blizzard is a business, there is clearly a huge incentive for them to charge you for transferring heirlooms across realm.
There is no technical reason why you can't transfer heirlooms, not a valid one. They own the servers, they own the databases, they own everything. Whenever you create a new character, you get a pet waiting for you in the mailbox, why not heirlooms? Just have the heirlooms waiting for you in the mailbox, who cares if they're duplicates, it's not like you can sell them or get extra damage because you have two chests.
Don't think of heirlooms as items, they're just numbers the same as anything else. There's nothing to stop Blizzard changing the way heirlooms work and instead of them being items, they just get flagged to your account. So let's say, instead of items in your bag, they're treated more like account flags, you access them using a button on your character sheet. You can then choose to invoke the flag (equip the item) or not, a bit like dragging glyphs from the list to the circle.
They don't even have to be items at all, why should you need to wear items to get the benefit? Wearing the same heirloom chest and shoulders, etc, everytime is boring. May as well just make heirlooms work similar to glyphs.
With all these things, there's nothing to stop Blizzard making them work cross-realm but if they did that, they would lose all the revenue from server transfers. A lot less people would transfer realm because with account bound heirlooms they would just level up again. And nobody would pay for mule character transfers. I paid for a realm transfer recently because I wanted to move my heirlooms, if Blizzard offered me the service free, I wouldn't have paid. And that's about the 10th time I've done it, and I'm just one single player.
So from a pure business sense, it's not going to happen. After everything Blizzard has done to create the miraculous and amazing game of Wow, I don't believe technical issues prevent me from using an item on another realm. I can even go to a website, type my credit card number in and buy a mount to use in game, technical issues didn't prevent that, did they?
Come on, be realistic.