why mourning for a parent extends beyond shloshim

1)Hard to believe that Elul is upon us already!  The Targum on the pasuk שְׁלַח־לְךָ֣ אֲנָשִׁ֗ים וְיָתֻ֙רוּ֙ אֶת־אֶ֣רֶץ explains the word וְיָתֻ֙רוּ֙ as וִיאַלְּלוּן -- the same letters as Elul.  The spies were sent to investigate the land and see what's what.  R' Schwadron in Techeiles Mordechai quotes from the Belzer Rebbe that this is our mission in Elul -- to investigate ourselves and see where we are holding.   The L Rebbe in HaYom Yom for 27 Av calls Elul   חדש החשבון. Just like a businessman needs to take stock and asses the the direction of the business, what is working and what is not working, so too in avodah and person has to do the same  דעל ידי הכנה טובה זו.. זוכים לשנה טובה ומתוקה בגשמיות ורוחניות.

2)  בָּנִ֣ים אַתֶּ֔ם לה׳ אלקיכם לֹ֣א תִתְגֹּֽדְד֗וּ וְלֹֽא־תָשִׂ֧ימוּ קׇרְחָ֛ה בֵּ֥ין עֵינֵיכֶ֖ם לָמֵֽת׃

כִּ֣י עַ֤ם קָדוֹשׁ֙ אַתָּ֔ה  לה׳ אלקיך

Is the reason for the issur of lo tisgodidu because בָּנִ֣ים אַתֶּ֔ם לה׳ אלקיכם or because כִּ֣י עַ֤ם קָדוֹשׁ֙ אַתָּ֔ה?

Simple pshat in the pasuk is that lo tisgodidu is an issur of cutting oneself out of grief while in mourning, but Chazal derive a secondary meaning and explain that it prohibits having different minhagim in the same community.  Maharal, as we once discussed, shows how these two issurim are related.  

Most of the meforshim explain that בָּנִ֣ים אַתֶּ֔ם לה׳ אלקיכם is the reason the  issur of cutting oneself, either as Rashi explains לפי שאתם בניו של מקום, ואתם ראויים להיות נאים ולא גדודים ומקורחים, or like Seforno explains  שאין ראוי להראות תכלית הדאגה והצער על הקרוב המת, כשנשאר קרוב נכבד ממנו במעלה ובתקות טוב. לפיכך ״אתם״ ״בנים לה׳⁠ ⁠״, שהוא אביכם קיים, but that begs the question what's כִּ֣י עַ֤ם קָדוֹשׁ֙ אַתָּ֔ה doing here.  See Ramban, Ibn Ezra.

Netziv suggests that the two reasons parallel the two issurim.   בָּנִ֣ים אַתֶּ֔ם לה׳ אלקיכם is why we should avoid having different minhagim in one community.  Because we are all "banim" and children of Hashem, we should behave harmoniously and each person not follow a different path (see Ksav Sofer as well).   כִּ֣י עַ֤ם קָדוֹשׁ֙ אַתָּ֔ה  לה׳ אלקיך is the reason to not harm onself in an outburst of grief like the anccient pagans used to do.  

In the sefer Meged Yesharim, R' Sorotzkin relates that he heard that when RYBS was sitting shiva for his wife, R' Hutner and R' Pinchas Teitz came to be menachem avel and the three began to discuss why it is that when a father or mother r"l passes a way, there is a full year of aveilus, but for other relatives the aveilus is limited to 30 days.  Shouldn't you expect the opposite?  Usually a parent is elderly, and so it's not such a shock when their time comes, but for other relatives, the same is not true.  Therefore, wouldn't it make more sense to allow for a more extended period of grief/mourning for the younger relative and less time for the elderly parent?

R' Hutner answered when one loses a parent, one has lost a generation that was closer to Sinai, and that is cause for greater aveilus. Rav Teitz answered that other relatives are replaceable -- one can have another child, find another spouse, one's parents can have more children.  A parent, however, can never be replaced.  R' Soloveitchik himself answered that davka because the death of a parent is the more natural occurrence, Chazal allow mourning for a year.  When death strikes a younger person, there is greater likelihood of the relatives being overcome by grief -- exactly what our pasuk warns against -- and so Chazal curtailed the aveilus to avoid that danger.  By a parent, where the death is expected, there is no such danger.  R' Sorotzkin suggests his own sevara as well, ayen sham.