I'd like to see this in poll form, although I'm sure its been done several times.
I took out Silvershard and Gilneas, although I think I'm going to switch out BfG for Deepwind Gorge. I go back and forth on SotA. I think it's a flawed BG, but I guess I don't mind doing it sometimes.
Silvershard,...I guess I just never really liked it. I don't know if it's being stuck in the cave, or the shape of it, or maybe just the whole mine-cart thing. So I've probably only done that battleground a handful of times.
Gilneas is ok, but it feels so small and stripped-down. I've had several fun battles there, but I think pugs get discouraged pretty easily if the other team gets hold of two or all three nodes. I'm not sure how much I've done BfG in Legion, but it seems like the mobility would make it worse.
Deepwind is kind of the opposite extreme for me. It seems really big and sparse, and most of the areas are pretty isolated from each other. And minecarts I guess.
I'm not wild about the big PvE BGs or the vehicular things, but I'll always love WSG, AB, and EotS can be fun too. Twin Peaks is cool because its CtF, even if the map is all goofy and crooked. I was skeptical at first about ToK, but I quickly grew to enjoy it's simplicity at the casual level.
In retrospect, I wish they'd made more battlegrounds that were Capture the Flag or Cap and Hold, but just on different maps (like BfG and TP). All the way back to Burning Crusade, they seemed to have the principle that every time they made a new battleground it had to be a different type of minigame, so we ended up with all of these battlegrounds with a panoply of convoluted objectives. They're often a barrier to fun PvP experience, because they're either a source of confusion (WTF is all this clutter and what am I supposed to be doing) or debate (three nodes vs 2 and flag), or because they sidestep the other players (IoC).