Oh, come on! You can entirely specify a cosmically hard problem in just a few kB. Prime factorization, anyone? Use discrete logarithms in finite fields, and you get down to handfuls of bytes.

Your conclusion is probably right, but your theoretical basis for it leaves a lot to be desired.

When you perform an internet search are you all by yourself consuming more computing resources than the i5 processor in your computer? That's unlikely, but you'd also have a difficult time replicating the functionality of Google with your CPU alone and only the storage on your own laptop.