You can, there just isn't enough Women competing.
Absolutely. Average woman's height is 5'5". If you're that height and physically fit, then with cutting weight almost everyone would get into the 135lb category.
Relatively few women fight - in all martial arts put together, let alone just one of them - so your pool of potential opponents is going to be small anyway. Add 'unusually tall/heavy' to the mix and your pool shrinks further. Size parity is really important for a fair fight; it's a rare catchweight where the little fighter wins. There just aren't enough 145+ women to have much interesting competition - even in Invicta, which has over 20 fighters in the division, there isn't really much fierce competition. Maybe as the popularity of MMA grows (it is MMA you're talking about, right?) this will change.
As you said they will likely be several pounds heavier by the time they actually come to fight so why do it in the first place?!
It's an arms race. The more weight you are able to cut, the greater your advantage over your opponent will be when you fight. ( Unless you cut so much weight that you are significantly more tired than they are) Part of the reason why Conor McGregor has dominated the 145lb division is because he does a massive, massive weight cut - but on the day of the fight he is taller and heavier than his opponents.
In the photo you can see how drawn McGregor looks at a 145lb weigh-in - it's not pretty. But in the other photo you can see the height difference between them. Officially, McGregor had a 4" reach advantage, but that advantage would be greater still in practice because his height means that his shoulder starts off closer to Aldo's face than Aldo's shoulder is to McGregor's face, iyswim.
When McGregor faced Nate Diaz they weighed pretty much the same, and without the size advantage it was a very different story.
But the whole weight-cutting thing is pretty controversial and I think that the rules will change as time goes on and we learn more about how it affects the body. The UFC has banned the use of an IV drip to rehydrate in order to discourage harsh weight cuts. Several fighters have moved up a weight class since - all to the good, imo. I believe there is some evidence that hard cuts can affect a fighter's susceptibility to concussion, so an end to weight-cutting is probably a good thing.
I just got hugely overinvested and checked out some stats on McGregor's record. All the people he has beaten (that I could get the info for) were shorter than him, except for rising star Max Holloway, who took him to a decision. All the people who beat him were taller. I think I have just found my betting system