The way you described it looked like trolling, hence the downvotes, I think. But your thinking is sound. People most commonly count their alcohol in shots and shot-equivalents.
1.5oz = 44ml. Most liquor is 40% ABV. That's ~18mL of pure alcohol.
The average beer bottle size is 330mL - 500mL, at 4-6% ABV. Again, that's in the 16-25mL of pure alcohol range.
Maybe rounding to 20mL might be a better definition of a "unit" of alcohol. It's still easy enough to do math with, and more representative of what people consider one drink.