As you say, I think whether/how to display the label is a rendering question, not an issue with the dataset itself, although I see your point. The Lake District is very heavily labelled.

I can see your point about it being a collection of hills rather than an area. The tagging as natural=mountain_range doesn’t seem wrong to me, but I guess an alternative would be to add a relation containing all the relevant hill tops and label that instead. Perhaps a type=site relation would be appropriate?