People understand that they can transfer money with their phones, and it is paid off at the end of the month (like a credit card) or comes out of their Pay as you Go balance (like a debit card).
With many prepaid debit cards, it would be easy for someone who found it to use up your remaining balance without getting caught, and you may be less likely to get your money back than you would be with a traditional credit or debit card that was reported as lost or stolen.
If you just need basic checking, bill pay, ATM access and a debit card, search for accounts that don't charge fees if you're below a minimum balance or fees of 25 cents or more for each check written.