"...meaning women need to get paid more per trip."
No, that's assuring equality of outcome rather than equality of opportunity. If operative A is spending 50% more time driving and thus is better at the task from practice, or from working unsociable hours, then there is no justification in giving operative B an artificial increase in pay to match operative A when operative B is not as good at the task and chooses not to work unsociable hours.
If you want to pursue the equality angle then the one valid point you put in there is a note about domestic demands. There is no good reason that such demands can't fall equally on male and female parents and is indeed a social trope that can be addressed (again, equality of opportunity; this time for men).
Also, please note its not women but those who *identify* as women, or would you choose to disadvantage males who identify as women? Tell you what, if I could get paid more for writing down on a job application that I identify as a woman, I'd do it.
We need to stop giving undue advantage to social groupings and start making sure everyone has the same opportunities to succeed regardless of gender and such.