Transferring data over Wi-Fi is more efficient than going over a cell network. With how many network services exist on phones now days, your phone can spend a lot of time doing network transmissions. Wi-Fi is more efficient for this, thus the savings.
You can see this in good cell phone reviews, they'll have a battery life test for Wi-Fi web browsing and another one for 4G web browsing, the Wi-Fi test will demonstrate a much better battery life.
Another way to think about it, is if you are in an office building that doesn't have cellular antennas places throughout it, then to connect to the cell network your signal has to get through the building material. If there is Wi-Fi available, odds are those antennas are close by and easily reached.
(Of course really noisy Wi-Fi environments can change the math on all this, but I do not know by how much.)
You could use a geofencing app to handle turning wifi on/off (say at home and work, etc) but then you are just trading battery issues.
Additionally, at least on android, wifi scanning improves location services. At least for me those are important, specifically when I am not at home or the office.
I’m not sure if that case exists anywhere in the civilized world. Subways and trains all have 3G networks, buildings have them, even in rural areas every 3rd tree you pass is a hidden 3G tower.
I don’t think I’ve seen a place without 3G anywhere in Germany in my lifetime (but I’m only 20)
It also significantly reduces the time to get a location, where satellites can take minutes to acquire (at least that was the case, back when I worked with GPS at that level)
This is taken care of by google, so I never connect to a network/sign-in, etc.
Edit: To be clear I'm not questioning your statement. Just curious to hear where Fi takes advantage of this.
There are several other places where it doesn't use the network unless I explicitly select it though (eg most Philz coffee locations, my work, etc)