Admiral Harward declined the offer, for a number of reasons HE cited, including family obligations. Less discussed was Admiral Harward's request to be able to name his own Staff, which was not agreed to sufficiently by the White House, at least in their preliminary discussions.
The fact that General Flynn did nothing wrong, per the President, yet his resignation was sought by President Trump (and others in the WH Staff) had to be a giant red flag for anyone considering tossing away a lucrative current job, doing what he likes to do for lots of money, and throwing his lot in with the new Administration without choosing his own loyal staff, is not remarkable.
There are others far more qualified than Susan Rice, for instance, who will do this job well, and the vetting will continue to find a good fit. Meanwhile, we have very competent people in place, and no shortage of talent in the current Acting General, who is very competent in his own right.