1. This is the last man standing, but there are women still standing. In which case there are still persons providing this service and it is not newsworthy.
2. This is a legacy saying from a period where only men could be involved in business enterprises. There may have been women running such businesses, but they are not worthy of record.
If not 1, then the correct phrase is “last person standing”.
The issue is not whether the last person standing is male or female. The issue of “last X standing” is about all the Xs except the last one.
Honestly, I’d be fine just treating this (and similar) as skunked terms. Last man standing is gendered and old fashioned. Last person standing is clunky and weird.
Over-inclusivity serves no purpose in this situation. It makes the language clunky and needlessly unspecific.