The most significant downsides are psychological and kidney stones, plus its literally (by definition) your body’s signal of starvation.
https://en.wikipedia.org/wiki/Ketosis#Safety
Oh and this gem from the article on starvation.
> After two or three days of fasting, the liver begins to synthesize ketone bodies from precursors obtained from fatty acid breakdown. The brain uses these ketone bodies as fuel, thus cutting its requirement for glucose. After fasting for three days, the brain gets 30% of its energy from ketone bodies. After four days, this may increase to 70% or more.[11] Thus, the production of ketone bodies cuts the brain's glucose requirement from 80 g per day to 30 g per day, about 35% of normal, with 65% derived from ketone bodies. But of the brain's remaining 30 g requirement, 20 g per day can be produced by the liver from glycerol (itself a product of fat breakdown). This still leaves a deficit of about 10 g of glucose per day that must be supplied from another source; this other source will be the body's own proteins.
This is the biggest reason I've never done more than toy with ketosis is the body consuming muscle for protein to supply that remaining 10g of glucose per day. Esp. because 1 lb of muscle only 1,800 Cal vs 3,500 Cal / lb. Fat.