Desirable properties of a future KDF

These need to be configurable
With settings encoded along with password hashes, etc. - depending on specific use case
Tunable high-level and instruction-level parallelism within one instance
Barely sufficient if the KDF is sequential memory-hard, otherwise abundant will do
Ability to use almost arbitrarily wide SIMD vectors within one instance
Running time almost independent of password length
Existing hashes upgradable to higher iteration counts
without knowledge of the plaintext passwords
Maybe to higher memory cost and higher available parallelism as well? - tricky
Friendly to whatever hardware we have in the defender's system
and to hardware that we might have there in the foreseeable future