I think US$1000 for a 7 day stay is excessive.
Only small value purchases can't be done with a credit card.
What's more the point about taxis is specific to one firm and one card - something to do with not being allowed to charge more for a card over cash.
As noted upthread, the cost of the "convenience" is actually pretty low. When I go to Singapore it's ATMs all the way, but if you want some confidence, get a couple of hundred US$ changed into S$ before you go and take another $200 in greenbacks.
I really think you would have to go out of your way to get through S$75 a day in cash where credit card options will already exist.
Obviously the last thing you want to do is be left with a surplus of S$ at the end of the trip and be paying to convert back.