I think you are imagining an aligned allocator out of an unaligned allocator, where the misalignment should be stored somewhere around the actual memory block,

I think you are imagining an aligned allocator out of an unaligned allocator, where the misalignment should be stored somewhere around the actual memory block, but if the main allocator itself is aware of aligned allocations it is not necessary. I can still imagine the case where allocation bins are structured by the allocation size and alignment size and an incorrect alignment will result in an incorrect bin, but such bins are only beneficial when the alignment itself is too large compared to allocation sizes, and I'm not sure who really wants them in the first place.