So, yes, dates grown on palms in the desert can be dried. I can't even recall that the Romans, who had a mainly dry climate in the Med, had much dried fruit. They did use honey as a preservative for some fruit I think, but then the cost would have been enormous. Widespread consumption of dried fruit is mainly a modern phenomenon I think.
Dried plums being one of the biggest.
Apples of course store for a long time naturally so they probably were not dried as often but certainly some.
Cherries, berries, grapes, any small fruit was dried routinely.
I am not sure where you are getting this big "cost" idea. Fruit plus sun, dried fruit.