Validating the url
The motivation is a small performance gain, with the rationale that some hash-pluggable algorithms do not rely on full-length pre-image resistance.
The proposal has met with significant negative feedback due to it creating a non-standard security assumption (compared to all previous hashes), and therefore it creates risk and all hash-pluggable algorithms (like HMAC, RSA, DSA, hashcash etc) would need to be re-examined on a case by case basis to see if SHA3 is safe to use with them; from the balance of the feedback it seems probable that NIST will accept the feedback and SHA3 will retain the full 256-bit pre-image resistance.
A full hash inversion has a known computationally infeasible brute-force running time, being O(2^k) where k is the hash size eg SHA256, k=256, and if a pre-image was found anyone could very efficiently verify it by computing one hash, so there is a huge asymmetry in full pre-image mining (computationally infeasible) vs verification (a single hash invocation).
A second hash pre-image means given one-preimage x of hash y where y=H(x), the task is to find another pre-image of hash y: x' so that y=H(x').
Pre-computation advantages would perhaps be enough motivation to replace the hash with SHA3.In the original 1997 algorithm hashcash used SHA1 because at that time, this was the defacto and NIST recommended hash, and the previous defacto hash MD5 had recently started to show signs of weakness.Bitcoin being specified/released in 2008/2009 uses SHA256.The idea builds on a security property of cryptographic hashes, that they are designed to be hard to invert (so-called one-way or pre-image resistant property).You can compute y from x cheaply y=H(x) but it's very hard to find x given only y.