Yes, it seems to be the right solution.
As suggested here, binding the docker binary itself is not needed and could create problems. I was convinced that it was required but it's not the case!
⚠️ Former versions of this post advised to bind-mount the docker binary from the host to the container. This is not reliable anymore, because the Docker Engine is no longer distributed as (almost) static libraries.
Yes, it seems to be the right solution. As suggested here, binding the docker binary itself is not needed and could create problems. I was convinced that it was required but it's not the case!