This is only a problem if you naively undersample the normal maps in your fragment shader. No AA algorithm can can generate a high quality result from undersampled lighting calculations.
MSAA also doesn't require you to have only one color sample for each pixel but this can be varied per draw call (at least for desktop GPUs) - effectively allowing you to supersample some objects when needed.
For normal maps specifically, you can preserve lost information from downsampled normal maps as roughness: https://media.steampowered.com/apps/valve/2015/Alex_Vlachos_...
MSAA also doesn't require you to have only one color sample for each pixel but this can be varied per draw call (at least for desktop GPUs) - effectively allowing you to supersample some objects when needed.