- Coins can be animated in a more interesting way to give more life to a game (like rotating in some of the Mario games). How do you animate money sacks? Gold bars? (Maybe, flashy with glitters, but the result may not be good with the graphics capabilities of old hardware). Note that in the original Mario Bros I think (not sure, need to double check) the coins may bounce on a platform, which could look out of place if you use sacks and gold bars. (For bouncy coins, check also Fantasy Zone. The sequel added banknotes, but I think it didn't work as well, and it took me a long time to realise they are banknotes).
- Coins are easily recognisable, especially on primitive video hardware. To convince someone a sack contains money, we usually draw a dollar (or pound, yen, whatever currency you're using) sign on it, which may not be easy for a small sprite on hardware with limited resolution and colours. For gold bars see the glittering comments above.
- It is more natural to connect coins with interesting and funny metallic sounds, e.g. the sound made by collecting coins in SMB. I'm not joking, but some analyses did mention the satisfactory feeling gained by hearing the sounds of collecting coins repeatedly was one of the reasons for the success of the game. That Nintendo later even used it in their logo should tell you something.
Edited to fix some of the typos since I was in a hurry and used a list for easier reading.