What would've made more sense is to plan a transition from BT to a new era. Have him stay on for one more season, have the contracts of everyone involved expire along with him, then start with clean slate and a fresh hire. This doubly would've made sense as the new AD would be in place and the Board of Trustees would've been up and running for quite some time by then. All parties could've coordinated with one another.
Prospective coaches around the country would've known about the vacancy a full year in advance, and would've been given the proper autonomy to take over the program. The university would've drawn a lot of interest in that scenario. It would've been an attractive situation for a coach to walk into, especially if BT was on board with the plan, and if the hire could be done early enough as to not impact the recruiting season.
That'd be much better than conflict, half measures, and chaos.
What I see here is a Board of Trustees that were impatient and rushed to push BT out, while the administration was not yet prepared or equipped to handle the transition. The pieces are not working together. In the end, it led to hard feelings from the man who deserves the lion's share of credit for making the Huskies a successful team in the first place.
Next time the Trustees are planning for a drastic change in direction, they shouldn't enact that change in late December. Set the organisation up for success rather than failure. It is all too easy to blame the admin, but I don't believe that the admin planned on replacing BT in the first place, so the Trustees must share in the blame for this botched process.