The system would still work if everyone decided to switch signs like you said. But it would be confusing without standardization, so we've all agreed that Debits are positive and Credits are negative.
Plus, switching signs doesn't make it any easier to understand as a whole. A simple example: You're Blockbuster and a customer gives you $5 to rent a video.
Cash +$5
Income -$5
If we switched the signs, now our Income would be easier to understand (changed to a positive number), but Cash would be negative (and more confusing - why would it be negative when we received cash?)
Plus, switching signs doesn't make it any easier to understand as a whole. A simple example: You're Blockbuster and a customer gives you $5 to rent a video.
Cash +$5
Income -$5
If we switched the signs, now our Income would be easier to understand (changed to a positive number), but Cash would be negative (and more confusing - why would it be negative when we received cash?)