It appears a trade off inherent to that feature. 
Technically (paraphrasing from memory), I suppose the device goes in such a deep sleep that it takes longer till the WiFi is enabled and till the device has connected with the AP. Whereas when that option is put to Always then it keeps associated with the AP and the WiFi chip doesnât go in such a deep sleep. Neither Yes or No is the best setting, though Google defaults with Always On by default. (Which conveniently also suits their data gathering.)
You could opt for selecting âWhen Chargingâ as well. Personally (going a bit off topic here) I try to not charge my mobile devices too much, and keep the battery between 30% and 90% to preserve it. Although with a FP2 the battery is only 20 EUR + S&H, and easily self replaceable. If I want to conserve my battery I just put WiFi off or Airplane mode on. LTE I practically always have off whilst home/work or at friends. You may also wanna disable all kind of apps you never use. I liked Stefanâs suggestion here Should smartphones carry health warnings? with a so-called detox guide. Day 6 is concerning cleaning up smartphones but a few other days also contain relevant info. Thereâs also a bunch of other threads on the forums concerning power saving.