There's a cycle path near me a bit like that, that's shared with the pedestrian path in places. It's set back from a major road, and there's a series of side roads into residential areas that the cycle path crosses a few feet back from the side of the main road. As a result, cyclists have to pretty much stop dead at every side road and check traffic from in front, to the side, and behind, because cars turning into or out of the side roads have right of way. All it takes is one car forgetting to signal and you're on the deck, or worse. Staying on the road, which as far as I'm aware is perfectly legal despite the occasional counter-claim by drivers of white vans, is a hell of a lot safer even if you don't factor in the sections that are shared with pedestrians.
Dave