Well they didn't use a search firm last time, and took some criticism for it after the fact. So that's why they're outsourcing the process this time.
From ESPN:
[FSU Athletic Director David] Coburn said the university would hire a search firm to help find a new coach, and the Florida State boosters would also play a role in the decision. Former Florida State athletic director Stan Wilcox did not use a firm when he hired Taggart in December 2017. Wilcox stepped down from his job to join the NCAA eight months after he hired Taggart, and after a lengthy athletic director search, Florida State opted to go with Coburn, who came over from university administration.
Besides financial considerations and the notion that any new coach coming in won't be given enough time to rebuild, what could complicate the coaching search is long-term stability at the top. Both Coburn and Florida State president John Thrasher are not expected to still be in their positions in the next two to three years. The newly created Florida State University Athletics Association, which now includes both the athletic department and Seminole Boosters, adds a wrinkle that hasn't been a part of any previous coaching search. Coburn said the new FSUAA wouldn't have a huge impact on the way the search is conducted, though he did say the Boosters would be involved.
Ideally you'd like your Athletic Director to be someone with lots of NCAA connections and the ability to conduct their own coaching search. But Coburn "came over from university administration," so probably doesn't have those resources.
Then there's the fact that, "Coburn and Florida State president John Thrasher are not expected to still be in their positions in the next two to three years." That being the case, might as well let candidates deal with third-party interviewers. If Coburn and Thrasher are leaving then the candidates are going to take any long-term assurances from them (about facilities, job security, future support for the program, etc.) with a grain of salt anyway.