Right!
For a representative example of ALL POHs consider;
The "805' of ground roll and 1440' Total distance to clear a 50' obstacle" (distances interpolated to 15 degrees C from the '78 172N POH specifying Vx TO distances at 10 then 20 degrees C) using a "Lift Off" speed of 52 KIAS and speed at 50' of 59 KIAS.
1) I have difficulty eye balling correctly 750' vs 1,000'. Am I supposed to go out and tape of the distances to the nearest foot??
2) If you subtract the ground roll distance from the total distance you would think you had the distance from "Lift Off" to the obstacle, but if you take the arc Tangent of the 50' divided by that distance you find the angle is always LESS than the Vy arc SINE angle of the Vy climb rate over the Vy KCAS - so Vy has a steeper flight path angle than Vx??
3) Of course not, so ALL POHs leave out the technique supposedly used to clear 50', most likely: lift off at just above power on stall (which incidentally is not specified in any POH), stay in ground effect until reaching 52 KIAS, then pull up to 59 KIAS.
4) If by some miracle you actually duplicate whatever the technique was to clear 50' (assuming there actually was one) do the wheels roll over the top of the 50' obstacle? or is there some unstated safety factor inherent but unstated in the numbers, e.g. is it really 60', or maybe 55' ?
There are many other omissions and commissions in POHs, this is just one glaring example of ; "If you want to know the actual performance of that commercially manufactured airplane, plan on spending 20 to 50 hours flight testing it yourself."