There are many variables that could lead to soft bricks. How well they were made, water damage, and overall age.
As far as morter. It is crumbling due to age and other factors such as moisture.
The professional suggested what is necessary, plus I would find out about replacing any soft bricks.
The tuck pointing will extend the life of the chimney. I would find out how long the professional has been doing tuck pointing, and look at a job he did more than 5 years ago. This kind of job seems straightforward, but its always not that simple.