This seems to parallel לא יאונה לצדיק כל און - No wrong shall be caused for the righteous, certainly according to Rashi (there on the verse and other places) that this applies to all sin, but even according to Tosfos that this only applies to food or things which are degrading for the Tzaddik, it is certainly appropriate to ask for that protection.
Note in a similar way, the Arizal says (brought in באר היטב on O.C. 447) that anyone careful about a Mashehu of Chametz on Pesach will be spared from sins the whole year, and the Lubavitcher Rebbe explains (Sichos Kodesh 5740 Achron Shel Pesach) that this refers to שוגג only, as free choice is not removed from the person.
So the point being it is possible to get divine help in avoiding accidental sin, and this is what we are asking for. Since we see that it is something that Hashem clearly does for deserving people, it is something worthy to ask for.
As for the last part of the question, you can't chose to do a Shoggeg. Rather you choose to ensure that your circumstances and actions prevent one. If a situation happens that was preventable but potentially leads to a sin, whether or not it actually does is up to Hashem. He can prevent the improper preparation from leading to a sin, thus forgiving the improper preparation.
(Parenthetically, I doubt it is humanly possible to prevent all shoggegs in everything in life. That is why there is a concept of לא יאונה לצדיק כל און - once you have done what you can do, Hashem takes care of the rest).
With a Meizid, you can ask to be forgiven, you can ask to not be tempted, but you cannot ask to be stopped from doing it, as that is your choice. With a Shoggeg, you can still do the things you shouldn't have done, and still be prevented, because your choice wasn't to do an Aveirah, it was simply to do something that could have not been done and avoided the situation. But since you have no control over if the situation will actually lead to an Aveira, you can ask that it not actually go there. This is a form of forgiveness, for sure, but it is a more powerful one, as it prevents the sin in the first place.
Or put another way, to use the other example, the food could turn out to be Kosher, at which point the whole sin is avoided. That is what we are asking for. Not to be prevented from the things we chose, but from their consequences.