We didn't start/stop at 15 knots for an arbitrary reason. We're actually pretty proud we can do 15 knots! You need a really specialized airspeed indicator to get below 20 knots. Airspeed vs. pressure is not linear. For instance:
5 knots is 0.0006 PSI
10 knots is 0.0024 PSI (4X 5 knots)
15 knots is 0.0053 PSI (2X 10 knots)
20 knots is 0.0095 PSI (2X 15 knots, 16X 5 knots!)
At 20 knots, the difference between 20 and 21 knots is .01PSI, which is actually much larger than the total pressure at 5 knots.
So the issue is that we need to be able to read 300 knots, which is 2 PSI. In order to resolve 1 knot at 5 knots, we'd need to be able to resolve .0003 PSI, while also resolving 2 PSI at the same time.
This is why a lot of airspeed indicators in something like a Cessna 172 start at 40 knots. Technically, we turn on at 20 knots as you speed up and turn off at 15 as you slow down. Of course, on the ground, wind gusts can make this flicker on and off.