When they banned alum in flour, industry and customers did scream. Today we find it very normal that our flour not contain alum. Alum makes whiter bread and consumers wanted whiter bread, paralleling what Pepsi is saying today.
Atkins-style diets have their downsides. especially in regards to blood pressure. Eating paleo sounds great, but remember that few of our ancestors expected to live past 30.
Life expectancy in pre-modern eras may have been around 30-ish years, but that mostly reflects extremely high levels of infant mortality. If you could reach adulthood, you usually expected to die around 50-60.
Only at the beginning if you already had big, BIG troubles with blood pressure. The salt intake required might take you over the edge before your body adapts to ketosis. But only in those extreme situations and at the beginning; after keto adaptation you will excrete a huge amount of your salt intake rather than absorb it like you would otherwise.