Are there other foods that you think would be improved by adding a melting feature?
In other words, if ice cream didn't melt as you held it would you improve it by adding melting?
Because "part of the fun" to me sounds like a knee-jerk justification rather than a real evaluation of whether it's a good thing.
Butter and chocolate are solid at room temperature; likewise ice cream is served frozen. Part of what makes all of them so pleasant to eat is that they melt rapidly in the mouth, pleasantly coating the tongue.
Many foods become "not quite right" when butter is replaced with another fat, and lack of melt-in-the-mouth is one of the reasons.
I don't think that you can say that melting is objectively better, but I think it's an intrinsic property of the food.
It's definitely a subjective preference.
I dislike everything about the fact that ice cream melts rapidly under most conditions. To me it's inconvenient and destroys the original structure of the thing I want to consume, forcing me to accelerate the speed at which I consume it (or end up with a milk drink). I think I'd ideally reduce the melting speed by between 1/2 and 3/4.
And there are frozen, custard-y desserts which don't melt. Yet ice cream is #1.