This is my experience, too. Without autonomy and ownership across a whole project it's very easy for people to get tunnel vision about what's valuable. This causes general harm to both the team and the outcome of its project.
I'm not sure how to lessen the effect other than perhaps by making projects small enough that they can be worked on by just a few people and using this phase to establish a kernel of good ideas and team cohesion.
Perhaps there might be another structure where the tools that are provided to the team are literally so good that the main project can be done by just a few people working on everything together. (Idealistic vision here.)