This is just the way the algebra shakes out. The upper bound comes from the following condition: in equilibrium, it will not be more profitable for any chunk-only producer to switch to being a block producer. The lower bound comes from the symmetric condition: in equilibrium, it will not be more profitable for any block producer to switch to being a chunk-only producer.
In the lower bound case, the terms involving BP quantities (like D_BP / S_BP) cancel out which results in a cleaner expression. In the upper bound case they do not cancel out, so there are chunk-only producer quantities which remain.
The reason things cancel out in one case but not the other is because there is an inherent asymmetry in the setup in the cost term. In both cases the cost term takes the form (x-1)C, but it appears on different sides of the inequality in the different cases. It is clear that x - 1 >= 0 and C >= 0, so the lower bound on (x-1)C is also 0. When this cost term is on the smaller side of the inequality we can simplify the expression by replacing it with its lower bound (ie 0). When the cost term is on the larger side of the inequality we replace it with its upper bound, which comes from the condition that chunk-only producers are profitable (we could instead use the condition that block producers are profitable, but this does not help in simplifying the expression). When replacing the cost term with its upper bound we pick up the extra terms ultimately stick around until the final result.