Good post. A different perspective.
I think your post is entirely valid except for 3 big reasons as I see them.
Much as it was clear Postecoglou just wasn't up to the job, 17th isn't just down to a manager and his coaching team.
Secondly, I think Frank would want 2 or 3 players who kind of came in with him. Just implies a certain bond and those he can get answers from re: murmurs within the squad, etc. I think its also a display of being backed by the people who employed you.
Fans thrive and live off the buzz of new signings. It adds volume and belief, especially when they are considered high grade.
If Frank cane out straightaway and as soon as he signed and said I dont want new players because I want to give th current squad 4 months to assess them, and will only seek to replace first-teamers who leave - fine.
I like the gist of your post. I think the risks would be there for many to see.