score:5
Besides more global solutions like http://www.onesimcard.com, there are no 'local' sim cards for multiple South American countries, comparable to Africa's Airtel.
On top of that, South American cellphone networks tend to be somewhat fractured, meaning that out-of-the-way locations might only be served by one, or a few, of the nation's networks.
So, with a foreign sim card, you might be able to use multiple local networks, but, indeed, at a cost.
If you expect to use your phone extensively, your best bet is to get a local sim card. However, also keep in mind that some countries will require you to register the card with the equivalent of a local social security number. (I don't know whether Ecuador, Peru, Chile or Bolivia need this, but Brazil most certainly does.)
But, some personal experience, I spent quite a few months traveling around South America last year and this year, I never really missed not having a local number. Wifi access is almost ubiquitous. And in places where it isn't, cellphone access tends to be an issue as well.