Apart from what both Abhijeet Singh and C.A. (Kees) Kan have stated, crushed egg shell raises the KH and stabilizes the pH when used. The change in KH or the stability of pH might convert some metals to biologically non-responsive states and may not take part in the phytoremediation at all.
I just want to mention that it is a general misconception that egg shell changes the pH in soil.
The reality is egg shells are very stable compound which do not decompose easily. And since they do not decompose, they can not change the pH of soil. However, pH change might occur in the acidic soil, where soil organic acids react with egg shell compounds, mostly calcium carbonate and neutralize the pH. it might also occur in the soils with high organic matter where the decomposition of organic matter produced organic acids which could react with egg shell. So, in most of the cases adding egg shell powder is not much of a reclamation. Nevertheless, egg shell powder might increase the porosity of the soil (depends on the particle size)
I never mentioned the use of eggshell to change soil pH. It stabilizes pH. The funniest part is my statement was made for the use of eggshell powder in water as it has been used for many years in various aquaculture as well as Stability of pH and ascendancy of KH were explicitly mentioned. If there are misconceptions then I'm glad that I don't seem to suffer from one.