Ethereum uses the Ethash hash function for proof-of-work. It was designed specifically for this purpose by Vitalik based on previous work by Thaddeus Dryja.
The main rule they teach you in a crypto class is: never roll out your own crypto. Why not take any of the existing memory hard hash functions? From scrypt used in Litecoin and its forks to any of the PHC competition finalists (also, Zcash later chose Equihash, designed by the authors of the PHC winner, for its PoW).
I did not find any academic papers with cryptanalysis of Ethash. This analysis elaborates on why password hashing and PoW are not entirely the same task, but still gives no rationale for designing a new algorithm.
Ethash serves its purpose well for now, but what if a critical vulnerability is found? For a recently developed algorithm without years of cryptanalysis behind it it seems likely compared to more established alternatives.
What was the rationale behind choosing to design a new hash function for Ethereum's PoW?