I wouldn't sign that. Sure, you can define homology groups for simplicial complexes pretty easily, and it makes stuff computable, which is great. Here is why I still think this doesn't make anything trivial:
1. Computations can be damn hard, and if you do them using a computer, you might miss out on a lot of insight and geometric intuition. 2. More crucially, if you have a topological space and represent it as two different simplicial complexes. How do you prove that the homology groups are the same? I don't know if that is approachable from the simplicial point of view, and I guess it would contain pretty terrible book keeping. Very far from trivial I guess. This is where singular homology really shines: You prove that simplicial homology is isomorphic to singular homology and don't have to worry about that ever again. Also functoriality only works if you have maps which preserve the simplicial structure, whereas singular homology has no such restriction.