Can't he just take another chariot? Can't he just fight on foot?
It's his trying to lift the chariot is the reason of his defeat.
Can't he just fight on foot?
That's exactly what he did. Standing on the ground, Karṇa fired several astras including the brahmāstra on Arjuna which Arjuna countered with his own.
Chapter 1216 (66)
But, in that great battle, the earth swallowed up one of the wheels of Radheya's chariot.
Radheya wept in rage. He told Arjuna, 'O Pandava! Wait for an instant. You can see that because of destiny, my central wheel has got submerged. O Partha! Abandon the thought that only befits a coward. O Arjuna! One should not shoot a weapon at one with dishevelled hair, at one who doesn't wish to fight, at a brahmana, at someone who has joined his hands in salutation, at one who has sought refuge, at one who has cast aside his weapons, at someone who faces a calamity, at someone who doesn't have arrows, at a person whose armour has been destroyed, or at a person whose weapons have been shattered and broken. Brave ones do not strike at such people, nor do kings and lords of the earth. O Kounteya! You are brave. Wait for a short while. O Dhananjaya! Let me extricate the wheel from the ground. You are stationed on your chariot. You should not kill me when I am on the ground. O Pandaveya! You and Vasudeva are not frightened of me. You are a kshatriya and you are the extender of a great lineage. O Pandava! Remember the instructions of dharma and wait for a short while.'
Chapter 1217 (67)
Sanjaya said, "Vasudeva was stationed on his chariot. He said, 'O Radheya! It is fortunate that you remember dharma. Quite often, when they are immersed in hardships, inferior ones censure destiny, but not their evil deeds. O Karna! When you, Suyodhana, Duhshasana and Shakuni Soubala brought Droupadi to the assembly hall in a single garment, did dharma not show itself to you? When, in the assembly hall, Yudhishthira, who was not skilled at dice, was defeated by Shakuni, who was skilled at dice, where did dharma go then? O Karna! During her season, Krishna was under Duhshasana's subjugation in the assembly hall and you laughed at her. Where did dharma go then? O Karna! Resorting to the king of Gandhara and coveting the kingdom, you challenged the Pandavas. Where did dharma go then?' When Vasudeva addressed Radheya in this way, Pandava Dhananjaya remembered all this and was overcome by great rage. Energetic flames of anger seemed to issue out from all the pores on his body and it was extraordinary.
On seeing this, Karna again invoked brahmastra against Dhananjaya. He showered down arrows and tried to extricate his chariot. Pandava countered those weapons with his own weapons. Kounteya then released another weapon, beloved of the fire god, towards Karna. It blazed fiercely. Karna pacified the fire through a varuna weapon. He covered all the directions with clouds and it was as dark as a rainy day. Pandaveya was not frightened. While Radheya looked on, the valiant one used the vayavya weapon and dispelled all the clouds. The supreme one's standard had the marks of an elephant's housing. It was decorated with gold, pearls, jewels and diamonds. It had been crafted by excellent artisans over a long period of time. It was expensive and beautiful in form. It always inspired your soldiers and terrified and frightened the enemy. It was renowned in the world and blazed like the sun and the moon. Kiriti used a razor-sharp arrow that was gold-tufted and pointed. With that, he brought down the handsome and blazing standard of the great-souled maharatha, Adhiratha's son. O venerable one! When that standard was uprooted, fame, dharma, victory and everything that was dear to the hearts of the Kurus also fell down. Great sounds of lamentation arose.
To ensure Karna's death, the Pandava took out an anjalika arrow...
It's his trying to lift the chariot the reason for his defeat.
No, as I explain in this answer, it was a fair fight after all. Arjuna's firepower was just too much to handle for Karṇa.