I think there are too many types. I don't use 10¢, 50¢ coins, nor do I use $2 $10 $50 bills. Why?
I think what I want is for each size to be 4 or 5 times as big as the previous size. My simplicity-preferring brain doesn't like to see a $2 bill when two $1 bills is not that much more to carry. I don't like to use a $10 bill instead of two $5 bills. Carrying five $1 bills is a bit much and then I'm happy to carry a $5 bill instead. Two or three isn't enough to trigger this desire; four or five is enough.
If we started with 1¢ and stepped up by a factor of 4 or 5 each time, then the sequence would be 1¢ 5¢ 25¢ $1 $5 $20 $100. These are the ones I actually use in practice. For Euros we could have 1c 5c 20c €1 €5 €20 €100 €500.
Let's drop 10¢ coins and $10 bills and treat them like 50¢ coins, $2 bills, $50 bills — they exist but we don't use them widely.