Pawpaw/papaya/lechosa (as they're called here) are delicious - but unless you're preparing raw papaya salad, they have to be perfectly ripe. Otherwise, as you so rightly point out, they're almost tasteless.I didn't like them when I lived in Europe though. Thought them boring and one-dimensional in taste.
A popular way to use them in Venezuela is as a drink - often a mixture of pawpaw and orange juice. Really refreshing.