Mate, there are limits of reasonableness and I think your suggestion would be crossing them. These sites are quite remote and scattered all over the continent.

You can also walk right up to the base of Uluru, you're quite mistaken about how protected it is: https://parksaustralia.gov.au/uluru/do/walks/uluru-base-walk...

You can walk the entire perimeter as a man or a woman without restriction.