It seems yes there is a reason if you need integrals. From TFA: "You can also try having Wolfram Alpha compute it, and it will time out. We will need to be more creative."
Mathematica/Maple don't have freemium timeouts because they are not free; Sagemath, OTOH, is a good point.
You would never figure out that black holes are a solution to the Einstein field equations of you just threw a numerical solver at it, for example. (Bad example because that's arguably the easiest solution to them but I hope you get my point.)