Firstly any FEA is only as good as the operator, secondly I've run Solidworks and it's FEA module on an old HP laptop, it works just fine, just takes a little longer. You don't need the latest laptops/PC's to run FEA.
Presumeably you can calculate stresses etc using hand calculations? If not you shouldn't be using FEA.
Any tool is only as good as the user. That is a given.
Did I say you needed the latest laptops/PC's to run FEA? No, I didn't. I just said that it's nice to have the cloud take the bulk of computational load if you so choose.
Also, why on earth would you waste time calculating stresses by hand for anything other than the most basic geometries when you can use FEA and have it done it a fraction of the time. I could make all the parts I machine at work with a file and a hacksaw if I wanted, but why would I?
Hopefully my response is useful to the OP of the thread.