Shove and throw don't work like this in D&D rules-as-written
So, you've practically made a wizard with a fighter build... And it's the game fault that your fighter-wizard is capable of doing the fighters things? Great work at proving nothing but the fact that D&D allows you to built your character ignoring his class needs and act as a weaker version of another class.
Fighter doesn't even get to shove and throw like it can in Baldur's Gate 3. Niara is talking about how the homebrew mechanics supersede any class's skillset. Choosing the wizard class is an experiment on how over-tuned Larian's homebrew is.
