Buddhi discerns; ahamkara personalises. Where the first evolute registers a judgment about the world with no reference to anyone in particular, the second evolute is specifically the tattva that attaches a self to that judgment: not merely "this is painful" but "I am in pain," not merely "this is desirable" but "I want this." The literal meaning of the Sanskrit, I-maker, states the function without decoration; ahamkara is the machinery by which an impersonal cognitive event becomes a personal experience.
This appropriating function is what makes ahamkara, rather than buddhi or manas, the tattva Samkhya treats as the immediate root of bondage in practice, even though buddhi is where the discrimination that ends bondage eventually occurs. It is ahamkara's claim, "this body, these senses, this suffering belong to me," that purusha is mistaken for endorsing, and it is that specific mistake, rather than any change in purusha itself, that the whole soteriological program exists to correct. Ahamkara is not, on this account, an illusion to be eliminated; it is a real tattva doing real work, misapplied only insofar as it is taken to define purusha rather than merely to belong to prakriti's evolving apparatus.
Ahamkara's productivity is what makes it structurally central to the twenty-five tattvas: everything from mind and the senses to the gross elements traces back through it, so a system that wanted to name the single busiest principle in the entire chain, after prakriti itself, would have to name ahamkara.