Presumably a key reason it is recorded on entry to the lounge is to know where to look if the flight is closing and a pax hasn't shown up at the gate? And probably for charging purposes too as I assume pax from other OW carriers all cross-charge each other for access?
Yes, those are both good reasons for recording lounge entrance. I have also experienced some polite comments after entering BA Flounge at T3, some 15 minutes after passing AA FL. And yes, I had some polite comments about where I spend the most of time waiting for the AA flight.