You can "beg" all you want. As of December, 2010, the percentage of U.S. residents with cellphones (measured as "household cellphone penetration") was just over 96%. And 27% of U.S. households have cellphone service ONLY, without landlines. Sure, there are still some Luddites out there. But next time you are at WDW, take a look around. Try and find a family that does not have at least one cellphone amongst the group. I don't know a single 13 year old who doesn't have a cell, let alone an entire family.
But leaving cellphones aside, there are many ways to notify a restaurant that you are not going to show up. Again, look at the original post. The entire premise was that the meal might be missed because the park is going to be crowded with long lines. If one is waiting in long lines, one has the time to find a way to extend the courtesy to the restaurant that the reservation should be cancelled. Will the world end if you don't? No. But that is not the test of when one should act courteously.