Half Bloods are there for fun, and that's all. Yes, there is no real reason to farm them, but if you're fed up with the limited number of Elders, False Gods, and all the similar decks in the Arena (the place where you'd expect the most diversity in decks.. heh) you can 'relax/take a break' with them because they're actually really fun to play against - and I believe a game is more about fun than mindless grinding. You'll never know what you're up against next; sometimes their decks just doesn't make sense at all, but occasionally they can be real scary and hard as hell.
I've played HBs exclusively for many (~5) months back then, when there was only Elders, T50 and FGs for grinding purposes - mainly to keep my interest in Elements -, as I've found T50 too repetitive and False Gods unfair. When I took a major break for the first time, I've ended up with +80k score and countless +rares and upgrades, so actually "farming" them does pay off after awhile. Of course, now that we have Arena (and even more powerful shards and card combinations) this score/electrum gain seems like a joke, especially after the amount of time I've spent to achieve it, but at least I had fun and it kept me around.
They are also great for testing decks against Gods and higher leagues; and maybe even for some of the newcomers too (the ones that are not introduced instantly to the overused deck archetypes through forum/chat), preparing them for all the 'unfairness' they will face later in their Elements career. I think they are fine the way we know them, and the fact that you have that slight chance to win upgraded cards makes them even more entertaining.