Not necessarily. There are many use cases where there is no disadvantage to a fast hashing algorithm. For example, secure hashes are commonly used to guarantee that data has not been modified. (I believe that PHP uses a hash for this purpose, as it is much faster than running rsa on the entire message.)
What this REALLY tells us is something that we have known for a long time: fast hash functions are suboptimal for password "storage"/verification. We need to use something slower for dealing with passwords, such as bcrypt, which can be made arbitrarily expensive.