Intrigued by this mention.
Anything that balances shot chance closer sounds reasonable.

Randomness on shot scoring is fine.  If a GK makes a dozen saves then so be it.  It happens in real matches sometimes.
But it would be demoralising if you on wrong end of lower shots than expected, and this was repeated every other week or whenever, it would feel like a kick in the stones.   Weighted change sounds good as a fair-play leveller. 

Late kick offs in the cup today due to tedious clock change to help farmers or whatever the reason.

A nonsense.  😝