Actually, it was Bhima who made the vow that Arjun would kill Karna and Sahadev would kill Shakuni. Therefore, they had to fulfill it, since he was their elder. While Karna may have been unmatched by the other Pandavas (aside from Bhima), Shakuni could have been slain by any of Draupadi's kids as well: it didn't have to be Sahadev.
Yeah, Bhima made that oath, but anyone could have killed the Dhartarashtras. For instance, Dhrishtadymna, who lost every one of his battles against Drona, Kripa, Ashwatthama and Karna, easily defeated Duryodhan on day 18 and forced him to flee from the battlefield. If he could do that, he could have killed any number of Kauravas.
On the Chakravyuha penetration, it required a skill that only 4 warriors had - Arjun, Krishna, Pradhyumna and Abhimanyu. But just b'cos Arjun had a certain skill that Bhima didn't didn't make him an all-round superior to Bhima. Also, Jayadrath had a specific boon from Shiva that he'd defeat 4 of the Pandavas on a given day, but not Arjun. That wasn't due to Arjun's superiority: it's b'cos Shiva had already given Arjun the Pasupathastra, so he couldn't bless someone else that Arjun would be defeated.
Remember, on day 14, Arjun lost a lot of time fighting Drona, and ultimately, Krishna persuaded him to just bypass him w/o necessarily subduing him. Yudhisthir later sent Satyaki, and then Bhima to find out whether Arjun was safe. When Bhima fought Drona, he broke 100 of his chariots before passing him, which Arjun either couldn't or didn't.
I know Bhima made that vow that's why he killed 100 Kauravas, does this mean none of the brothers or warriors in Pandava's side were able to kill even 1 Kauravas? I think they left them for Bhima to fulfill his vow
Skills people acquire by hard work makes them superior, Arjun worked hard to get weapons and train himself, Arjun's absence from Kurukshetra had landed them on back foot, Duryodhana would have won on that day itself, if not for Arjun's son
Shiva gave Arjun the boon, If you know this then don't you know how Arjun acquired it? He defeated and satisfied Lord Shiva 🙃
Didn't Arjun vow to kill Jayadratha before sunset or he will kill himself? On 14th day, there was a 3 layered formation to stop Arjun from reaching Jayadratha, There was 48 miles long Vyuh with 20 Mile diameter chakravyuh of Kaurava warriors for Arjun, which was led by Dronacharya, Everyone in Kaurava army was protecting Jayadratha to make sure Arjun kills himself, I don't understand why would they focus on an inconsequential part of Pandavas. Jayadratha wasn't in this Chakravyuh, he was being protected by Karna and Aawatthama along with more than 100k knights, 60k chariots, 14k elephant warriors, 20k foot soldiers, Arjun broke all layers efficiently to reach Jayadratha
The aim was to kill Jayadratha before Sunset, Arjun and Drona were in a never ending battle which would have led to sunset and Arjun killing himself, Therefore Krushna advised him to not waste time here and look for Jayadratha. Both Drona and Arjun killed thousands of men in chariot, elephants etc, Arjun would have been killed by Drona, if he didn't take down his support army on chariots, elephants, He was able to move ahead by destroying the layers of Vyuh only, But, Arjun couldn't kill Drona as long as he had a weapon in his hands.
In fact, Drona was so rattled he started killing normal soldiers with celestial weapons, which as against rule of war and they decided to kill Drona on Day 15
Arjun alone killed 7 Akshauhini force of Kauravas on 14th day
One more thing, Arjun had left Yudhishtira with Satyaki that day saying Satyaki has to protect Yudhishtira so he can fight battle without having to worry about protecting their King, There was a time when Dronacharya had almost captured Yudhishtira but Sahdev took him away, that's what happens in Arjun's absence.
Arjun had killed many key players on day 14, Arjun had defeated Duryodhana breaking his chariot and weapons, but Arjun didn't kill him, he could have easily done it but Bheema had vowed to kill Duryodhana. Similarly, Bheema did not kill Karn because it was Arjun's vow to kill him
One could imagine, how many warriors would be there to protect their King because Duryodhana's death means losing the war, Arjun had killed and evaded all the warriors who were defending Duryodhana.
Arjun was battling Karna, Salya, Vrihasena alone at one point Duryodhana had made sure none of the Pandavas reach Arjuna but Bheema and Satyaki get there, In the end defeating everyone in their purpose Arjun killed Jayadratha.
14th day of war shows how important Arjun was In the war of Kurukshetra, They couldn't defeat him so they did everything in their power to hide a man to make sure Arjun kills himself. Drona realizes this and he was focused on capturing Yudhishtira in Arjun's absence.
If one side in the war thinks that one person's absence can make the difference in result of the battle, tells to story of importance of that person. One side put all of their to make sure they hide one warrior so Arjun kills himself, You see all of the attacked him together, it wasn't to kill him, they didn't think killing him in battlefield was a possibility, that's how important was Arjun in war of Kurukshetra