My question is more or less the opposite of this one: Why would one ever want to bother finding a natural primary key in a relation when using a sequence as a surrogate seems so much easier.
BradC mentioned in his answer to a related question that the criteria for choosing a primary key are uniqueness, irreductibility, simplicity, stability and familiarity. It looks to me like using a sequence sacrifices the last criterion in order to provide an optimal solution for the first four.
If I hold those criteria to be correct, I can reformulate my question as: In which circumstances would one ever consider it advantageous to complicate one's life by looking for a unique, irreductible, simple and stable key that is also familiar?