Yanky,
Were that the issue, would there not be a problem with *any* Yom Tov falling on Friday or Sunday. After all, one is not allowed to bury a body on Yom Tov* either.
We could live 2 days with total issur milacha if we had to….
Do you really think you could have gone two days without cooking in a world without refrigerators, supermarkets and the like? I’m not so certain.
The Wolf
* Of course, we’re talking about the first day of Yom Tov only.