And the fact is that while bonds are seriously overvalued (as the negative yields and the huge unservicable debts they constitute make them entirely non-productive assets, just false safe haven assets that only central banks either buy or hold these days), stocks in aggregate are a functional, productive asset, as they represent real business interests making real profits from real economic activity. So, once the real economy has absorbed the price inflation it has been sheltered from these past 8 years, stocks could make a considerable come-back from where they were talked down to (in this near-term scenario).
You are right when you say that bonds are more overvalued than stocks. Bonds are in the biggest bubble of all time. It's also true that stocks can generally be classified as a productive asset and that overall they will offer some protection against price inflation.
However, considering historical averages, stocks trade at very high valuations as indicated by the price/earnings relation. So stocks may absorb a portion of the coming price inflation, further rising nominally. But they won't absorb the whole inflationary effect.
Not all stocks are created equal of course. Companies in the service sector will perform worse than companies in the raw materials and manufacturing sectors.