After reading the same reasoning in Nagarjuna's Treatise on the Provisions for Enlightenment I decided to write about it.
To become a Buddha, and not merely liberated, one needs an infinite amount of merit. The only way to generate an infinite amount of merit is Bodhicitta. Why?With but a lesser accumulation of merit
One remains unable to realize bodhi.
Only by collecting merit more massive than a hundred Sumerus
Can one succeed in achieving that realization
Although one may perform but a minor meritorious deed,
Even in this, one possesses a skillful means:
Taking the sphere of "all beings" as the object,
One should generate a mental transformation of the conditions.
Where one reflects: "May whatever actions I undertake
Always be done for the welfare of beings,"
Who could measure the merit of he
Whose mental actions are of this sort?
Imagine if you generate the desire to heal one person's headache. You would generate merit. Imagine if you generate the desire to heal five person's headaches. You would generate the same merit times five. if you generate the desire to heal everyone's headaches, since there are infinite beings, you generate an infinite merit. If you generate the desire to free everyone from all suffering and give them every happiness, you would generate even more infinite merit. This is Aspiration Bodhicitta.
Imagine if you actively engage in healing one person's headache. You would generate more merit than from merely desiring it. And that merit would multiply in the same way. If you actively engage in freeing everyone from all suffering and giving them every happiness, you would generate infinite merit. This is Engaging Bodhicitta.
So this is why Bodhicitta is so important, it's the only way to create enough merit to become a Buddha. This is also why Mahayana was taught by the Buddha, Bodhicitta is the only way to create enough merit to become a Buddha.