Arizona is not running out of water. There's a lot of fearmongering surrounding water levels at Lake Mead or with the Colorado river, but Arizona doesn't get the majority of its water from those sources. It also uses 10x less water with a population of 7m as it did in 1950 with a population of 0.7m.

Arizona has a state-of-the-art water portfolio that uses lots of reclaimed water and is not reliant on micro or even macro-climate trends. A megadrought has impacted the area for the last few decades and only now are Arizona cities talking about the needs for conservation and possibly cuts in the next decade or so, but if climate models hold up the drought will be over in that time frame anyway.

No, Arizona is not running out of water. https://www.arizonawaterfacts.com/water-your-facts

Is it plentiful enough that extracting highly-pure water is an economically-solved problem in Arizona?

What is the longest and (large enough) volume water piping system in the world? From my recollection its not long enough to significantly make inroads to another state.

edit: I think I might be wrong, looks like China has done significant waterworks across their country.

Why isn't it the same as say an oil pipeline? Those can get really long.

Oil is significantly more valuable than water - the added cost per gallon of water would be astronomical.

1 oil barrel is 42 gallons and costs around $75 today. I pay about $6 per CCF of water which is 748 gallons. It might be worth doing this with oil, but even if you scaled it up, it would be hard not to have the transport cost more than the actual water.

It would be cheaper to just desalinate it.

Of course Arizona doesn't really have that option. But California does, and Arizona already sources water from the Colorado River, which California does too.

Anyways. I think moving California off the Colorado River would do a lot to ease the water problems in the southwest.

California has had trouble kick starting desalination. It is an energy intensive process, and the California electricity grid (especially in water poor SoCal) is still heavily dependent on fossil fuels (even some coal plants in other states feed into the LA metro). Furthermore, desalination intakes can negatively impact marine life, unless subsurface wells are used. Those are more expensive and companies pursuing desalination are not eager to foot the bill for them. Perhaps most importantly, desalination (even without subsurface wells) is more expensive than current sources of water in Southern California. I've not even mentioned the challenges in achieving safe exhaust of brine.