A few thoughts on Moshe's request for Hashem to appoint a new leader:
1) "Vayidaber Moshe el Hashem leimor, 'Yifkod Hashem... ish al ha'eidah.'" There should have been no mystery about who the new leader of Klal Yisrael would be. Chazal tell us that Eldad and Meidad prophesized that Moshe was going to die and Yehoshua would lead the people into Eretz Yisrael. According to another Midrash (see below) Moshe thought his own kids might be worthy of taking the reins from him (not sure whether you can get these two Midrashim to fit together). Whatever the case, Moshe could have simply chosen whoever he thought fit. Yet that's not what he does. "Yifkod Hashem... ish al ha'eidah" -- Hashem, you choose. M'lo ha'Omer writes that an appointment by Moshe would have meant the new leader was a shliach of Moshe. Moshe wanted more than that -- he wanted the new leader to be the shliach of Hashem. That's a completely different level of leader.
2) "Vayidaber Moshe el Hashem leimor…" Why does the pasuk add "leimor" here? This is a private conversation between Moshe and Hashem -- there is nothing to communicate to Bnei Yisrael?
Rashi explains that Moshe not only made the request, but he wanted a response from Hashem -- "leimor" here means Hashem should say something back. (Rashi on "Va'Eschanan el Hashem...leimor" lists one other place besides that pasuk and ours where Moshe demanded a response. However, there are actually five pesukim in Chumash, as the Midrash notes, where Moshe makes a request followed by "leimor," so you have to figure out why Rashi only quotes three.) See Ohr haChaim as well here.
3) The Midrash writes that when Moshe heard the parsha of the inheritance of bnos Tzelafchad he thought to himself that it was time to consider his own children's inheritance. When he asked Hashem to appoint a leader, it was his own children who he had in mind. (The pashtus is that Moshe's request is linked to the previous pesukim, where he was told by Hashem to climb up Har ha'Avarim and look out over Eretz Yisrael because he was going to die without reaching the land. It sounds like Moshe is being given notice that the end is near, and so he begins to think about find a new leader. Why the Midrash ignores the obvious link to the previous pesukim and instead links this parsha back to bnos Tzelafchad is something to think about.) Hashem responded to Moshe that his children were not up to the task because they had not dedicated themselves enough to learning. Instead, the leader would be Yehoshua, who for years had served as Moshe's faithful helper.
What was Moshe's hava amina here? Did he not know his own children's character? Was Moshe no different than every Jewish parent who thinks his/her child is a genius, until Hashem comes to him and tells him kah mashma lan that they are not?
Rabbi Rakeffet tells the story (I hope I have it right) of the students who asked R' Aharon Kotler back in the day whether on Shabbos they could walk around with their suit jacket draped over their shoulders or is that carrying. R' Aharon answered that the bachurim in Slabodka used to wear their jackets like that and the Alter never said anything, so it must be OK. He didn't pull our a Shulchan Aruch or dig up a Mishna Berura -- R' Aharon simply knew the din because that is what he saw by the Alter.
The Ksav Sofer says something fascinating here. Moshe Rabeinu's kids grew up in the home of Moshe Rabeinu. So what if maybe they were not beki'im in every Shach and Taz -- they knew what was right because they got it through osmosis! They lived with and saw a living, breathing Torah. (I find it fascinating because the Ksav Sofer might as well be writing about himself. Of course he was a gaon olam in his own right, but he also grew up in the home of the Chasam Sofer absorbing Torah through osmosis.)
It's a nice hesber of the hava amina, but now you have to struggle a bit to explain why Moshe was in fact wrong and it was Yehoshua who was meant to take over. (See Ne'os Desheh from Ishbitz for a different hesber.)
4) Moshe asks Hashem to appoint a leader who will take charge in times of war and in times of peace (see Seforno), "V'lo ti'hi'yeh adas Hashem k'tzon asher ain lahem ro'eh," so we should not be like a flock with no shepherd.
It's clear from the beginning of his request that Moshe wants Hashem to give us a strong leader. What does he add by saying we should not be like "a flock with no shepherd?" (See Netziv)
If you understanding this pasuk, then you understand what a Jewish leadership is all about. Explains the Sefas Emes (5648), the shepherd of Klal Yisrael is only the Ribono shel Olam. Sadly, we don't always realize that. Sometimes we as sheep wander off. Sometimes we are not even aware of the presence of the shepherd guiding the flock. We think we are all alone, exposed to all kinds of dangers, when really we are being watched over every minute. Moshe said to Hashem, "Please give Klal Yisrael a leader who will help them realize they are not a flock without a shepherd."
True leadership is not about saying, "I'm in charge." True leadership is about making people aware that Hashem is in charge. "Hashem ro'i -- lo echsar…"