Suppose the leaf was giant.

And suppose the algorithm would attempt to add a new cell \$$x\$$ at the fringe of this giant leaf.

\$$x\$$ needs the standard rate of fluid flow to support it. Call this flow amount \$$y\$$.

Now \$$y\$$ would have to be added to the flow through every pipe on the path from the root to \$$x\$$.

Suppose there are \$$N\$$ pipes along this path.

Since we said the leaf was giant, this means that \$$N\$$ is large.

Were \$$\alpha\$$ to be close to 1, then adding \$$x\$$ to the leaf would incur a large cost, because all of the pipes along this long path would need to be widened.

But when \$$\alpha\$$ is small, this hardy matters, and it is no problem to feed \$$x\$$ through a long chain of pipes -- so \$$x\$$ gets added, and the leaf continues to grow,