Here's another cycle path example. And it shows why I find it hard to be dogmatic about these. This path is really a bit crap. its a footpath that has had some bike signs added and nothing else done to make it suitable for bikes. The surface is poor, it's very narrow in places, there are some overhanging trees that hit you in the face and a couple of farm gateways where it just disappears.
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But all the same, I sometimes use it. Depends on the time of day, how I'm feeling and what direction I'm going, the weather, how much traffic there is etc. Up ahead in the picture is a R turn that I don't like. I often pull over to the left and wait for a gap in the traffic because moving to the centre of the road can feel risky because of the closing speed of some vehicles from behind. So if I'm tired, it's the end of a long ride, not far to go, I'll opt for a quiet life and take the path. But early in the morning, with little traffic, no R turn, and I'm not tired I take the road.
In short: It depends.