Well I suppose I don't really see this hand to be vulnerable. There is flush draw that we also block somewhat. So 8 club which come 18% of time. Not such huge deal.
Ah sry 7 clubs as we probably don't hate Tc. I agree with maximum protection line with some set, two pairs or some Txxx which I would be happy to stack off with such low SPR.
If we want to stab some of air type low equity hands (e.g. some double paired hands come in mind as first ones) that are behind AAxx I would want to keep some of stronger hands like this in same range. Now maybe we don't want to bluff with those. Then going for pot seems totally fine with whole betting range.
Or maybe we look for max exploitation and only bet small with air. Yeah balance is not crucial as villain is unlikely to exploit us anyway but personally I don't want to do ton of lines that are totally unbalanced. Neither learn to do such lines blindly at least.
One example of total unbalance in holdem would be absurdly huge c-r on board like 8885A where I will simply always have quads and 80+% of opponents are incapable to fold Ax. But that is also ultra rare situation.