It is a common held assumption that problems with many objectives are harder to optimize than problems with two or three objectives. In this paper, we challenge this assumption and provide empirical evidence that increasing the number of objectives tends to reduce the difficulty of the landscape being optimized. Of course, increasing the number of objectives brings about other challenges, such as an increase in the computational effort of many operations, or the memory requirements for storing non-dominated solutions. More precisely, we consider a broad range of multi-and manyobjective combinatorial benchmark problems, and we measure how the number of objectives impacts the dominance relation among solutions, the connectedness of the Pareto set, and the landscape multimodality in terms of local optimal solutions and sets. Our analysis shows the limit behavior of various landscape features when adding more objectives to a problem. Our conclusions do not contradict previous observations about the inability of Paretooptimality to drive search, but we explain these observations from a different perspective. Our findings have important implications for the design and analysis of many-objective optimization algorithms.