Not a bad idea, although it sounds pretty similar to the wise old man in draynor. However, he only checks free-to-play. This would be somewhat helpful for members. What you should remember is that you don't need to hang onto every item you get from a quest (I did this once and had too much in my bank). Don't do that, pointless items such as burnt meat (from a quest), and things like satchels aren't important in anyway. It's simple to clean up your bank. Perhaps someone should suggest increasing bank space. I'm not completely sure why they wont do this, but something tells me it has something to do with java (just like the max amount of money).
The large number of different items will rapidly fill up bank space. This requires players to consider carefully what items they really want to keep in their bank. Reducing the number of different but similar items (food, armour, weapons, arrows, runes, etc.) helps to keep the bank tidy.
Even for members, a significantly larger bank space does not mean there is enough space for all kinds of items. In addition to managing the types of items that they keep in the bank, members often need to take measures to organise the items in order to reduce search time. Bank tabs have helped this problem significantly by giving players the option of organising their items in an easy way without all the hassle. The search function also reduces significant time spent searching for rarely used items within the bank.
Bank space tends to clutter up rapidly, as re-depositing a single item after closing the previous bank screen causes the item to be stored in an entirely different location. To avoid this, players can keep multiple items in the bank. For example, a player might keep two rune scimitars in the bank, so that taking one of them out will not affect its bank position. Of course, this does necessitate buying doubles of everything, and can be very costly for expensive items. Players might only have one item (such as quest items.)
I definetly agree.
But it might be useful to have an extra room or something, to store stuff when you have become a non-member. When you become non-member again, you cant store your skilled stuff etc. anymore. And when you take something non-member from the bank, you're stucked with it in your inventory untill you're a member again. You're forced to become a member again