Hmm. Rhen why does Apple recommend using WiFi for power saving?
“When you use your device to access data, a Wi‑Fi connection uses less power than a cellular network”
This is why general guidance for years was to use wifi when you are actually using your phone for browsing the internet, taking advantage of wifi's lower power efficiency when in use, but to turn off wifi when your phone is just in your pocket/idle to take advantage of cell network's better idle power efficiency.
However, the above is really only true for urban/suburban areas where you have good signal. If you are in an area with poor signal, your phone will use a lot of battery power via the cell network even when "idle" (because in reality even though your phone is "idle", the cell radio isn't actually idle, it's constantly struggling in the background to maintain the connection through the poor signal).
EDIT: Phones usually only transmit on one channel while receiving anywhere from 1-7 different channels at once, only the recent flagships transmit on 2 or 3 right now.
Nope. And the reason this is obvious is because turning off WiFi via the control center doesn’t actually turn off WiFi so collecting SSIDs wouldn’t be a problem either way.