So please tell me, why does a woman who is clearly in her post-childbearing years, or one who has had the removal of her reproductive organs, ALSO have to wait that same amount of time to get married? Why must a woman who was an agunah for decades, not be able to marry immediately (same as her ex-husband can), when she is finally freed, and clearly has not lived with him for WAY past those three months?
That’s actually a machlokes (Yevamos 42b). The reason for the shittah which is machmir (and we pasken this way – S.A. E.H. 13) is “lo plug”.
As for the rest of your post, right, that’s what I said. We can suggest a partial reason, but it’s much, much deeper than anything we humans can think of.