Why are there no defenders of the shrinking block theory of time - the view that the present and future exist but not the past? Here's one advantage of the theory: it gives a good explanation for a version of the 'thank goodness that's over' intuition. If I tell you that there is going to be an hour of pain in your lifetime and you can choose whether it's to be in your past or your future which would you choose? I bet, other things' being equal, you'd choose it to be in your past. But why? If Shrinking Block is true there's a good reason for so choosing: existent pains are a lot worse than non-existent ones.
Does Growing Block have advantages over Shrinking Block? Why be a growing block theorist? My old friend from grad school, Joseph Diekemper (currently Gifford fellow at St Andrews, and soon to be lecturer at Queen's Belfast) cites the fixity of the past and the openness of the future as reason to accept Growing Block. But his main target is the presentist: Joseph thinks the presentist can't account for the asymmetry in fixity because they have no corresponding asymmetry between the past and future. Well, this alone won't move the Shrinking Block theorist, because they do have such an asymmetry - it's just the other way around from the Growing Block.
Indeed, in some ways the Shrinking Block view seems more able to account for the fixity of the past and the openness of the future. The intuition to be saved, I take it, is that we can affect how the future will be but not how the past was. Well ask yourself this: what would it be easier for us to affect - an existent state of affairs or a non-existent one? Surely an existent one, since we can't even have causal interaction with a non-existent state of affairs.
I'm not seriously trying to get you to believe the Shrinking Block theory, of course. But I'd be interested to know just why Growing Block is meant to be a better option.