Why isn't $\ce{H2O}$ evenly distributed in Earth's atmosphere?
The brief answer is 'the water cycle' I think.

A longer answer is that water can exist in many states on and above the surface: at least snow, ice and liquid water on and below the surface and water vapour (gas) and aerosols of liquid water or ice (clouds) in the atmosphere. On the other hand $\mathrm{CO_2}$ can only exist in one: gas.

What that means is that $\mathrm{CO_2}$ is as well-mixed as any other long-lived gaseous component of the atmosphere over time, which is 'pretty well'.  Components of the atmosphere, such as $\mathrm{SO_2}$, which are not long-lived don't get mixed so well because they don't have time to be. For water the situation is even more complicated because there are complicated phase transitions going on within the atmosphere, and because the distribution of liquid water is extremely dependent on topography, and in particular it can move large distances from where it originates.

The phase transitions of water in the atmosphere are driven by temperature and pressure conditions in the atmosphere, and in turn alter those conditions, and the whole system is chaotic of course.  The result of some of these phase transitions is water leaving the atmosphere as precipitation.

How much water gets into the atmosphere depends on conditions on the surface and in the atmosphere, and also on where water is on the surface, which is extremely non-uniform (see above).

All of these transitions are driven by energy from the Sun which varies over the planet.

So the end result of all that is that


water vapour is not long-lived in the atmosphere as a result of all this, so it doesn't have time to become well-mixed;
water is not evenly-distributed on and below the surface because it's mostly liquid (and because snow &amp; ice is only stable in some parts of the surface);
the behaviour of water entering, moving within, and leaving the atmosphere is extremely complex and chaotic (or 'there is weather'), resulting in large variations over a range of scales in distribution of the various states of water which can live in the atmosphere, and large variations in how much water leaves the atmosphere over various scales.