One problem with this approach is that if you get lost, there is no way to get back on track... you are off-the-grid and into unmapped territory (literally!) quite quickly. Your map becomes useless and you really can't go back to your computer to print a new map with the missing details. In this case, ink savings gained pale in comparison to convenience lost.
More realistically, the counterpart of a LineDrive map in current route instructions is the list-of-turns representation: drive straight ahead for 12 miles, turn left into Whatever Ave., after 2 miles east turn right into Something St.
Once you allow for more space and include maps with details for all points of interest (i.e., all complicated intersections), both LineDrive and sequence-of-turns are only interesting as an addition, not necessarily as a replacement.
Another cool thing I like about Bing Maps: "Whole Foods on the corner" and "If you reach E 13th St, you've gone too far" when viewing directions. Such things would be cheered on as "look how awesome Google is!" if implemented in GMaps.
Also, the bird's eye view in bing maps always makes me go back to it, it's great to see what a neighborhood look like and how it would feel to actually follow a route. Google street view is just too zoomed in and too painful to navigate in to get a broad idea most of the time.
Yay! Back in the time I gave a seminar presentation on the LineDrive stuff. Pretty good combination of usability (show the user what he/she actually wants to know) and algorithmic stuff (automatic layout)...
More to the point, I always get lost with my own hand-drawn maps (when I'm too lazy to print one) and finally got better at finding places when I got myself a smartphone with GPS and OpenStreetMaps display.
If you still want this style of map and want to go completely analog, sign up for AAA and use their "TripTik" service (I think they still offer this on paper vs. only online.) You get a custom booklet with LineDrive type door to door directions on one side of the paper, and a 25 sq. mile map on the other side to give you context of where you are. The charming thing is you used to have to order this up about a week in advance of your trip, but I remember sitting in the front of the car with my Dad on family trips demanding to hold the TripTik and call out things we'd pass on the map.