The same reason why they gave away the formula to transparent aluminium - i.e. because who's to say it didn't happen that way?

ST4 really leaned into the whole time loop thing and I think that Gillian's disappearance was a predestination paradox as well - in fact her absence in the 20th century is probably why the whales went extinct in the first place, because she wasn't around to champion their cause.
So just like with the transparent aluminium, Gillian was useful to Kirk's mission, therefore he took her along without additional thought.
Or maybe he'd figured out that the timeline is riddled with time loops and therefore they were always destined to do what they wanted anyway?