I'd be surprised if squircles reduced user fatigue though - I think a good adjacent example is Googles new icons with the colours that all look similar. Users were complaining immediately that they had to look harder to find the correct app.
Another thing we use everyday - fonts - have differentiated visual spacing and shapes make them easier/quicker to read. So it would make sense for this to apply to icons that serve a similar purpose on a smaller scale.
For a moment there, you almost had us thinking that you were interested in learning something.