And yet they were at a loss on how to defeat him. Kakashi with his Sharingan eye was on the run towards the end of that fight. Not to mention that Kakuzu had a final form that he hadn't even used yet while fighting them. It was only after Naruto entered the battle and showed off his Rasenshuriken that Kakuzu decided to enter that form. Admittedly, Yamato had to keep Naruto from being impaled but that's all he did. Naruto specifically asked that the others let him handle Kakuzu, which he did with a powerful jutsu that even the 4th couldn't master.
Naruto trained to enter SM after Jiraiya died. He barely had time to recognize Kakashi's death upon his arrival on the battlefield. There were 6 Paths of Pain in total and Naruto defeated them all. Shall we count the ways? 1) an infuriated Naruto destroyed Pain's Asura Path with a Rasengan before it could attack Tsunade; 2) Naruto disposed of the Preta Path with Frog Kata before preparing the fruits of his senjutsu training: a perfected Rasenshuriken; 3) He hurled the attack at Pain's remaining bodies, and it expanded when it neared them, disintegrating the Human Path; 4) Realising that the Naraka Path had restored it, Naruto focused his efforts on getting rid of it by distracting the Deva Path with a smokescreen, and landing a great blow on the Naraka Path; 5) The Preta Path absorbed his chakra to make sure he was no longer a threat, but being unable to handle natural energy, the Preta Path turned into a frog statue, allowing Naruto to free himself; and 6) taking advantage of the five-second gap between its attacks, Naruto was finally able to defeat the Deva Path with his Rasengan and win the battle. You can find that all of that came from stated fact in the official Naruto wiki. At no point did he beg Kurama for power. Kurama tried to take control of Naruto through his angered emotions...something that was stopped by Minato as he replenished the seal. Also, Naruto defeated the final Pain with his Rasengan. There was no help from Kurama whatsoever.
I said "helped" because I recognize that Sasuke and Kakashi were the ones who were originally involved in the fight. However, Sasuke ended up being knocked unconscious by Haku's pressure point tactics. An angered Naruto is the one who got the upper hand on Haku while Kakashi is the one who killed him (accidentally mind you since he was aiming for Zabuza). Naruto is the one who ultimately convinced Zabuza to kill Gato and his minions. If you don't believe that then go back and rewatch that episode. Sakura didn't really do anything battle wise except for protect Tazuna.
Sasuke didn't really help defeat Gaara in my opinion. Yeah he pursued Gaara and initiated the fight but he was unable to handle the Sand Jinchuuriki. In fact, direct quote from the official Naruto wiki: "Naruto was put to sleep when the invasion began, but was awakened by Sakura so that they could go after Sasuke, who was pursuing Gaara in order to continue their fight. They caught up in time to stop Gaara from killing Sasuke." Note the bolded section.
Now to address your pain of loss argument. Real life example: I never knew my grandparents except for one. All the rest of my friends and family had a "complete" family meaning that they had 2 grandfathers and 2 grandmothers (one set on each side of the family tree). Do I miss my grandparents even though I never knew them? You better believe I do! It's the psychological pain of knowing that others have something you will NEVER be able to experience. Just because you've never had something doesn't mean that you can miss it, especially if you've had an inkling that it was once there. This is made worse if there are stories of these people. It only makes you miss them all the more. Plus, you keep forgetting that Naruto formed a bond with Sasuke which Sasuke subsequently broke in order to gain power. Naruto lost whom he considered a brother. That's pain of loss too.