I think this thread is a good example why mod actions should remain anonymous. Staff would get flooded with PMs asking why this and why that if it told them who did what. I often get posts asking why I moved their thread (from the incorrect sub to the right one) and half of the time it wasn't even me that did it. I think it's a plus that people even get a message informing them that their post is deleted because I've never seen that on any other forum I've been a part of. Normally your posts just disappear and you wouldn't even notice. I know it's frustrating and annoying whenever someone has a post deleted and nobody is going to like it but I think putting a mods name to it would be counter-productive. If people do feel like their post was deleted in error or malice believe me they'll make a thread like this about it and if staff were abusing their power in whatever way then they wouldn't last very long here.
You are correct in that it is better that mods are somewhat anonymous with their post removal in that you can't put blame on a particular person. A reverse of that is that a mod may not like a particular person and heavily moderate them for speaking out against certain policies.
To frame an example, a slew of about 5 posts about superhero's were deleted but the first one deleted was Biomech's and was the last of the few posts. My one posts about Ace and Gary, the ambigiously gay duo was probably the most racey but even took some days to get deleted with the rest. This says to me that the mods can be biased and heavily moderate certain people they do not like, while I agree with the forums rules that +1 posts serve no purpose, I would not agree with being unfairly targeted and having a personal bias.