All that removing currency would do is forcibly unite buying and selling, creating a dead-weight loss in potential economic gains made possible by the fungible nature of said currency. We'd be reduced to bartering for everything, which would discourage trade specialization and force all players to be generalists, meaning they'd be less effective at doing whatever it is they do to create value -- a problem which would be particularly exacerbated by the limited inventory space available.
Example: If I need bricks, and I make wheat, and you are the primary producer of bricks, but you only need oil, then I must develop competencies in extracting oil in addition to harvesting wheat in order to exchange with you. This would force my limited resources into two specializations, both of which will be, as a result, less effective. This is why currency was invented in the real world: to divorce buying and selling and to create a shared demand by which individuals with diverse goods may deal directly with one another.
Note: it also solves the problem of equitable exchange -- if I have a goat, and want firewood, and firewood is worth half a goat, either I have to buy twice what I need, or find a way to half the goat without destroying its initial value. Currency makes this a non-issue.
