Consider the switch from $$\operatorname{pH} = -\log_{10}\left(\left[\ce{H3O+}\right]\right)$$ to $$\operatorname{acidity} = +\log_{10}\left(\frac{\left[\ce{H3O+}\right]}{\left[\ce{OH-}\right]}\right)$$ in water.
I'm calling it "acidity" just so that I can refer to it below, don't worry about the name too much.
The neutral point is 0, when $\left[\ce{H3O+}\right] = \left[\ce{OH-}\right]$.
Acid solutions have a positive "acidity" instead of < 7.
Basic solutions have a negative "acidity" instead of > 7.
Both increase in strength as their value increases in absolute value.
The scale is open on both sides, which makes sense because there is no reason to restrict pH to [0, 14]. I know it's not restricted in reality, but for some reason I was taught that at some point.
In water, jumping from one scale to the other is as easy as $$\operatorname{acidity} = 2 \times (7 - \operatorname{pH}).$$
So why is that metric not used? I'm not a chemist so admittedly I have not seen enough chemistry works and maybe this scale exists, but in any case it's not mainstream while it seems like it would be easier to understand for the common folk.