Worthiness and Drive Times
Recognizing that you've come to a site called RoadTrip America where the people giving advice are all experienced and enthusiastic RoadTripers, the answer you're going to get to your first question, "Is this worth the drive?", is obviously: Yes. There is much to see along any route crossing an entire continent, especially one that goes through the Black Hills and Yellowstone, crosses the Rockies, and ends up on Puget Sound.
As far as how long it will take, you would need to devote six full days to driving roughly 500 miles a day. That is an eminently sustainable pace that you can keep up day after day after day and allows for two or three short stops each day to break up the workload. That leaves you four full days that you can devote to longer stops such as Yellowstone. So all in all, this a trip that can easily be done in ten days.
Other sites to "stop and see along the way" will depend on your interests and how far off your path you're willing to travel, but some that you should be considering would include Cleveland's Cuyahoga Valley National Park/Rock and Roll Hall of Fame/Natural History Museum; a sop on one of the Great Lakes such as the Bass Islands or Indiana Dunes National Lakeshore; Wisconsin Dells for the Dells, not the water parks; Badlands National Park; Devils Tower; the Little Bighorn Battlefield; and some of the many scenic byways in northern Idaho.
AZBuck