There is reasons behind these restrictions. The reason of low amount of gold are given, is just for not exploiting the loans. Players can borrow large amount of gold then send them to their main account or friend's account and then abandon the hero and his depth.
In past, bank was paying interest! But this allow players to keep no gold on them and there wasn't any point to loot someone. To force players keep more gold with them they turned bank to vault.
As for diamonds, there is no reason for safe keeping and since it's they way the company makes money to pay salaries and bills, there is no point for interest there, or logic, when the game gives you many free diamonds and an in-game diamond market for gold.