The separated bike lane *and* the mixed use path is the end goal, but if the immediate goal is to save the city money and make people healthier rather than create conflict and negative sentiment towards cycling, then you need a separate route for ebikes and more experienced commuters. Sharrows or magic paint suffice for this (at least temporarily) with adequate traffic calming or if the main car flow has an alternate route.
Imo, American negative sentiment and aggression toward bicycles is way more about politics and assumed demographics then anything else. It does not matter how well behaved average cyclist is. It does not matter how intrusive or safe it is. The people who are aggressive will focus on that one minor infraction that happened once to validate their anger.
I think we overall agree, but there are many things that can be done to reduce conflit points.
Firstly I agreed that the mixed lane with a shared car/bicycle alternate route should come first (as this covers both short/slow speed trips and high speed/high confidence trips), but secondly the shared lane has an absurdly small cost. Under 5% of the space and an even smaller fraction of the money spent on roads will give you a world leading bicycle network, and if you build it, it will be used -- cycling on good infrastructure is simply so much cheaper and more convenient than car ownership and cycle lanes have so much more capacity than roads that it becomes a no brainer.
I agree that bootstrapping it to get the political will needed for that pittance is extremely hard, which is why we need to think very carefully about encouraging long distance commuters who must average over 15km/h to make reasonable time and people taking the pram for a walk to mix. Ebikes are a big potential issue because they are both fast and favoured by new riders. It will only take one ebike with the speed limiter removed accidentally injuring a kid and hitting the news to set back bike infrastructure in an entire country by years.
Step 1 is mixed paths connecting local destinations (schools, shops, church, etc) and start reserving your space for the separated bikeway
Step 2 is a fully connected network where all the mixed paths have an alternate route with magic green paint or sharrows for high speed trips and to handle congestion.
Step 3 is build the separated paths.
You can't skip step 2 or avoid thinking about step 3 until it is too late.
Additionally throughout this process you need to fix all the cyclist and pedestrian hostile signals (waiting for a full 5 minhte cycle at a one way street full of stopped cars because the button wasn't pressed is absurd) and provide some alternative to stop signs (carefully designed roundabouts, yield signs, or cyclists-yield laws with public outreach work okay).
It is already difficult to have a car near house where you live here.
You complain that bike lanes are not used "enough", but a single parked car forces a whole lane to have a throughput of 0 commuters per hour. A bike lane that gets a single cyclist per hour is infinitely more efficient!