That approach works in cities that have established massive cycling communities - the Montreals and Copenhagens.
The mid-step approach for North American cities is an extra-wide bike-lane clear of the door zone with dotted zones that require drivers to shift into the bike-lane if they want to turn right.
Basically, the bike lane is effectively a "bike lane and right-only-turn-lane". It's less protected than the parking-protected bike lane, but it avoids the right-hook problem.
This way drivers will always see the cyclist when they wish to go right.
In urban areas with established cycling communities where you have enough density that cyclists are expected? There you do the parking-protected lane. In that kind of environment, cyclists are common-enough that drivers expect them and know to look for them.
My city (Hamilton, Ontario) uses both, and I get a lot more right/left hooks from cars on the protected lane than I do on the right-turn-plus-cyclist lane. The protected lane is a great endgame and we need to get there, but step one is "take the whole right lane and make it cycling/right-turn-only". It takes a lot of space but it's a great way to begin.
The problem is the popular approach is completely half-assed: the glorified shoulder in the door-zone, with no information for drivers about pulling over into the lane to turn. That leaves both the right-hook open and the door-prize.