The reason for recording a prepaid expense as a current asset is

To match revenue and expenses correctly (the matching principle - you should read up on it as it is one of the fundamental principles in Accounting). If you were to expense the item when it is for a period, the month it is expensed will have an understated net income and the other months will have an overstated income. By writing the prepaid expense off as it is used, you are correctly matching it to the revenue of the month in which it is expensed.