Linseeds/Flaxseeds.

I’ve seen it reported that one of the downsides of Atkins et al low carb regimes is the lack of fibre. I’ve also seen flax oil recommended as a supplement to balance the saturated fat that seems to be be implicit in these regimes. With this in mind, it would seem that flaxseeds are an ideal supplement because they are high in fibre and flax oil. Can anyone suggest why they are not generally advocated?