Ground storage of fresh water is a simple technique that people seem to resist. 'Controversial' is not the right word but in the permaculture community there is a definite divide between people who embrace it and those who resist. The interactions are... frustrating.
There's also a relationship between water, soil health and climate change. The rule of thumb is that an acre of land can store an additional 20k gallons of water by increasing the soil carbon by 1% (of overall fraction, not relative to previous carbon levels, so in most real world cases that may involve increasing carbon by 10-25%).
I didn't know it was controversial. In San Jose we have many (currently dry) ground water recharge ponds where water is let in for the purposes of seeping into the water table. Much of the city uses ground water, the resulting water is quite hard but has a decent flavor profile.
Some people think 'store water' and immediately jump to cisterns, or above-ground storage tanks. You simply cannot store a useful amount of water above ground, and exposing it to light and air (and thus mosquitoes) is a whole other set of problems.
Some people do it anyway, others get very upset about what they see as wasted time and resources.
Storing water [this way] is fundamentally about reserving the right to be wrong about where water 'needs to be' on your property, and I think without a way to correct it they feel like their hands are tied. The person I know who is loudest against this strategy is also very philosophical about not fighting nature. If a tree is happy, great. If it's not happy, then it wasn't meant to be. Let it go, get over the sunk cost, and try something else. To his thinking, trying things is cheap, forcing things is expensive (and arrogant).
Basically you want to slow the flow of water and increase the soil's permeability and retention capabilities. Beaver dams are a good way to start, but things like Hugelkultur burms, terracing and swales are all methods of capturing water run off and directing them into the ground where they can enter aquafers or be absorbed by the immediate soil.
These aren't large scale projects across rivers, but just enough to capture the run-off on one's own property. Mostly you are improving soil retention, and refilling the aquifer. Often times it's as simple as creating repeated depressions in the desert so that dust, seeds and wind blown matter can collect along with just enough water to start plant growth so that the topsoil can be stable once again.
Stopping is different from slowing. Slow water keeps streams from drying up in the summer. Lots of stories of seeps and seasonal streams coming back after years of having dried up.
There's also a relationship between water, soil health and climate change. The rule of thumb is that an acre of land can store an additional 20k gallons of water by increasing the soil carbon by 1% (of overall fraction, not relative to previous carbon levels, so in most real world cases that may involve increasing carbon by 10-25%).