Wolf,
I love questions like this, I guess because I read lots of science fiction when I was younger. I think one possible answer may well be in your questions themselves: “I wish I had not done that” and “I wish that hadn’t happened”.
If Hashem would change the past in response to our tefillos, then we would be provided an avenue to place responsibility for our actions outside of ourselves. I can imagine it totally destroying the foundations of teshuva. For example, I can imagine the following sequence:
1.) Person does an aveirah, realizes and regrets.
2.) Person sincerely asks for forgiveness, but davens that the sin never happened (erase it).
3.) Sin still exists in the past (e.g., in the person’s memory or through the consequences of his action).
4.) Person interprets this as a rejection of his tefilla.
5.) Person projects some responsibility for the situation to Hashem, after all, if the sin were really so bad in Hashem’s eyes, He would erase it.
Basically the person would become so past-oriented, obsessing over the erasure of the past sin, that he would lose focus on the present and future.
Here’s a question I had when I read your post:
If Hashem did change the past, how would we know?
From our perspective, we exist only in the present. We cannot affect the past (but the past exists in our context as memory/recordings/history and effects on the present), and the future does not yet “exist” for us. If Hashem changed the past in response to our tefillos and we were aware of this (somehow retaining awareness of the now non-existent timeline), then we would be able to affect the past in a way. For whatever reason we aren’t supposed to have this ability… or know about it, at least.
Personally when I read about true teshuva and how G-d enacts a miracle and erases our sin (as if it never happened), it makes me think. Is our perception of the past Hashem’s reality?