Surely Strachan was a manager of a premiership minnow/relegation favourite for many years, he was looking for a different job and went and took one. Burnley manager has a job, just got promoted and isn't looking to bail is he. He's got his own team, money to spend, and little pressure as most people will assume they'll be relegated, while Celtic are big budget, huge pressure and if he doesn't win the league he'll have to resign/quit.
But also remember that at the end of the day its a job, and his passion is Celtic, if he failed the club he loves, well its almost unthinkable so theres not really a huge amount of positives to take him there.
As for Ambramovich, people are jumping to conclusions about his lack of patience. HIddink showed the problem, managers after Mourinho had inherited a incredibly defensively minded team with few attacking options. Grant, Scolari, even Hiddink aren't really the managers for a defensive team, while Hiddink showed what he could get defensively against Barca, its not really his style and, he has a job.
Ancelotti is a much smarter appointment, a manager from a league thats more defensive in nature, someone who can work better with the current squad. Scolari in theory was a great appointment, but in reality he's had a team thats picked itself for brazil and required no motivation or teaching, club footie is completely different.
But it was clear where the economy was going while Grant/Scolari were there, he couldn't invest as he didn't know that he could afford it. AS the markets semi stabilising again, people are clearly on whats happening and chances of him investing are higher.
will help that Hiddink will tell him to spend no doubt, Hiddink's smart enough to realise they need wingers and a striker, will tell Roman, and he'll get his chequebook out. Lets also not forget that for 3 years Mourinho spunked hundreds of millions on players who aren't even at the club anymore, let alone those that Chelsea are stuck paying huge wages too still(kalou, Malouda, lost huge money on cocaine guy whose name I forget). he's got a incredibly weak squad for the cash spent and surely anyone in their right mind would want to find the right manager/team before spending again.