That seems like a good approach until you consider that you don’t know whether the results are unsatisfactory if you aren’t looking at both sets of results on each search. You can’t see what you don’t look at and you can’t know what you don’t know. Google may have a better result for you, but how would you know unless you search both engines?
“Unsatisfactory” is an opinion-based comparison. If you find something that satisfies your desire, it’s satisfactory. I’d say your argument is more based on whether the results are more accurate, or “better” in some more concrete way.