I find it useful for estimates on how long the journey will take, which I've found are usually accurate for a first go at the route.
However, I find TfL's free cycle maps (with recommended routes marked on them by cyclists and cycling organisations) to be far more useful in planning routes.
I too find the paper maps quite good, it allows you to work out your own route
My major issues with the tfl cycle route planner are:
* No allowance is made for hills, so you have some rather silly routes for example to get from A to B where the direct route along back roads may be the shortest (or the longest) however there is a 'cycle' route that runs via C at the top of the hill. You would have to be mad to take it.
* As the routes tend to have limited or no signage, you need the ability to follow the map, however the routes are so convoluted that even a a person, such as my self, with a bar bag to mount the map, a compass, many years of experience with teaching mountain navigation, ability to use a GPS and a good knowledge of London, still makes mistakes. How is a normal semi-map illiterate expected to manage to read a map, navigate and ride a bike at the same time ?
I agree technology may be the long term solution to this, as give it a few years even the average mobile phone will have basic GPS and map technology, and I'd hope the mounting brackets become as common a bells on the handlebars
* There seems to be very little use made of alleyways, paths, back routes, parks etc. all of which it's perfectly legal to cycle on