...their idea of strength training is next to useless--trying to max out once or twice a month in a major movement with no consistent practice between these efforts is absurd.
This is a very good statement. I've been told that the XF trainers spend a lot of time on correcting exercise form. However, if you look at some of the WODs, they rarely go over 60kg for stuff. If you are a 100# woman this works for a while, but not for anyone with a good amount of strength.
Even the ME Black Box stuff is way more suitable for experienced lifters than beginners.
The "mixed mode" stuff came from a similar place as the "Liftinov" stuff from Dan John. Do some lifts, then sprint off with a sled or pick up a rock and run for a bit. Simple, yet highly effective.
You'll get stronger, faster if you follow Rippetoe's recommendations from "Starting Strength". Notice that Rippetoe is the lastest "Strength" guy recruited for XF. He's got the XF-Wichita Falls thing in his WFAC gym as a kind of subset. I'm waiting for the fallout, because Rippetoe's not the kind of guy who will stomach bullshit.