Not sure if you have read AXE.
Here is a shortened version on the benefits of AXE type training:
The Best All-Around Training Method EVER | StrongFirst
In essence, as a standalone programming style it very minimalist all-around training, managing conflicting demands elegantly.
AXE is indeed power training. Sure, sprinting and olympic weight lifting might be more "pure" (max power if you will), but power training covers a range on a continuum (as shown in AXE):
GPP is defined in Easy Strength (looking forward to ES 2.0). Here is an short excerpt from an Ozolin quote:
S&S does all of that. AXE with only Swings does not, IMO, while AXE (KBSF) with LCCJ does. But you can always add some missing links. Adding some goblet squats, TGUs and endurance exercise (as recommended in AXE) would make your routine more GPP.