The reason you mostly read about pax doing this on connecting itineraries, as opposed to LAX originating itineraries, is that most would probably say it's not worth spending the extra 40 to 50 minutes walking back and forth to TBIT if you're not already trapped at the airport.

But if you have the time, and want to check out the *A lounge, there's nothing wrong with your plan. If you're going to check bags at T7 then enter airside at T4, suggest walking on the top level, as that's much more pleasant than the lower (arrivals) level.