"What is supposed to happen when you get to that busy road?"
At both main roads there should be proper crossings going in (I'd asked upthread about the one with the railing, appears the railing is coming out). So assuming decent light timings after pressing a button it could in theory be quicker than, say, arriving at the lights on the main road route just as they turn red. Also, for the final right hand turn to the Commie you won't have to queue with cars as there will be a dedicated segregated lane (and crossing). That will obviously then turn off to head to the Innocent, so you can either stay on the main road, or follow through St Leonards to pop out just below the Commie.
Timings really depend on lights, but I think once it's properly up and running there won't be much in it between the routes (road route maybe slightly faster); but obviously there will be the benefit of being away from traffic.
In fairness this is really a 'missing link' route for families or inexperienced riders, that allows them to access the Innocent while before they would have been put off by the road. By suggesting the route is too convoluted, and for that reason you'd rather ride on the road, I think that marks you out as someone that this isn't intended for in the slightest (which would apply to many on here, but not all).
I've started taking the off road path through the Meadows rather than the road just cos it's nicer, and if this link is done well (oh what an 'if'), I'll probably follow it round in preference to the main road.