A lot of teams have cap space and a "do everything" veteran big (and proven playoff performer) has a lot of value. So I wouldn't be surprised if he gets 4yrs and $100m from someone.
With all that said, Ainge is absolutely right not to match that type of offer. In fact, I think he's probably lucky Horford opted out of his $30m option this year.
Great player, but the age bothers me. Al isn't exactly ancient, but he will be 37 at the end of a 4-year deal. Let's be honest, the Celtics had to do quite a bit of load management with him last season, and there is some evidence he has lost a step. I think his athletic decline will accelerate in the next couple years.
Love Al, but I think whoever signs him to a deal like that may ultimately regret it.