The YAGI-UDA antenna has been known to be a good performer for a long time. It just wants to work, when correctly tuned. With the "ordinary" GAMMA-match there is mostly a matter of keeping the RF from the shield of the feeder. When RF-currents flow along the feeder, the antenna behaviour is badly affected.
A simple 4-5 turn coil of the feeder, near the feedpoint, makes an RF-choke that reduces this Feeder-Radiation.

The height of the Yagi is the spacing between the antenna element and something else than thin air downwards.
This is most often the true ground, with it's local dielectric constant and conductivity.
[Trees are thicker than air, but very hard to predict how they influence our RF-energy ; Solid wood or not so dense branches. As a rule of thumb, < 8 MHz You cannot see too much of an affection, but on > 10 MHz they affect somewhat, the greater the higher the frequency is AND with moisture content in the wood.]

The conductivity near the horisontal antenna is of less importance, what the low takeoff angles are concerned.
The conductivity affects almost only very high takeoff angles. [ Verticals {NOT VERTICAL DIPOLES} are HIGHLY dependable of the local ground conductivity though ].

Your surrounding neigbourhood is most important for the antenna behaviour. Most important is the actual antenna height over this area, out to some 10 wavelengths. For shortwave yagis it is more important to have it placed high up above the actual RF-ground, rather than high above the surrounding terrain. For the VHF-yagi it is more important to have it placed high above the surrounding terrain than over the specific RF-ground. The VHF-yagi is easily put up enough many wavelengths for the lobe to be concentrated towards the horizon and it is more sensetive for 'line of sight'-modes.

Why is antenna gain so important ? The ionsphere does behave in a non-linear mode at certain energy level. See propagation. It is sometimes vital on some distances to be able to concentrate Your antenna lobemax at a specific takeoff angle.

If You have reached to the conclusion that the only right antenna tower for You is a fully rotateable type, then You do not have to rely solely upon mother nature anymore.
You can vertically STACK at least two yagis of the same type, and control Your takeoff angle lobe yourself. This is done by means of how You feed Your yagis in or out of phase. If feed in phase, you will maintain the actual vertical lobe diagram of a single antenna at about the same height as the upper one, with the difference that the gain is enhanced due to that the lobes minima are made somewhat wider and the nodes stronger. If feed out of phase (180°) the lobe diagram will be totally different. Now the minima changes to the vertical angle where it had it's maxima in before, the nodes change the previous minima angle.

The above example is taken under the condition: Lower 0.42 lambda; Higher 1.27 lambda height above the RF-ground.
The in phase peaks at 14° and the out of phase peaks at 35°.