Use of analysis of mahAvAkya-s
The first question while studying anything would be about the utility of the endeavor. For e.g., study of medicine is important because it can cure diseases which cause pain. Why are mahAvAkya-s important? It's because they teach the unity of brahman and Atman directly and succinctly. So sureshvarAchArya says in Ma 2.12, tattvamasi-Adi-vAkyeshhu tayoH-aikyaM pradarshyate, i.e., by the sentences such as 'That thou art', their (jIva and brahman) unity is taught. He who sees duality sees great fear, whereas the one who comprehends unity does not. Thus the taittirIya says na-bibheti kadAchana-iti. It is also known that the inner self is shAntaM shivaM and advaitaM as per the mANDUkya upanishhad. So teachings of non-duality are certainly very important.
But the taittirIya upanishhad also says: yato vAcho nivartante, aprApya manasA saha - From which the speech along with the mind turns back, when talking about brahman. The various means of knowledge like pratyaxa (direct perception), anumAna (inference), etc cannot reveal the true nature of brahman, and only shruti has that capability. And sureshvarAchArya says about this particular inability of the pramANa-s  other than shruti in his NaiSi 2.1s: pratyaxAdInAM anevaM vishhayatvAt, teshhAM svArambhaka-vishhaya-upanipAtitvAt.h - Since the scope of pratyaxa, etc is different from this subject matter (Atman), and since their scope is restricted to the substances which produce them. He also adds: vastumAtra-yatha-athmya- prakAshana-paTIyasaH-tattvami-AdeH-vacasaH-eva-iti - i.e., *only* words like tattvamasi are capable of revealing the real nature of the self. To repeat, the indeclinable 'eva', i.e, "only", should be noted.
Thus, not only do the mahAvAkya-s produce enlightenment, they are also the *sole* means of achieving enlightenment . For the advanced student hearing the mahAvAkya alone (shravaNa) through the instructions of a qualified guru, is enough for the complete destruction of avidyA. But, even for the lesser qualified students the mahAvAkyas are of great importance because the shravaNa would lead to manana and nididhyAsana, which will finally lead to destruction of avidyA. In either case, the importance of the mahAvAkyas is established. The actual analysis of the vAkya-s, consisting of manana and nididhAsana is a must for most, except perhaps a handful of extremely qualified sAdhaka-s. The following material is on the analysis of mahAvAkya-s, as taught by sureshvarAchArya.
 The number of pramANa-s, whether they are 3 or 6 or more, is irrelevant to the topic under discussion.
 The term "achieving enlightenment" is used synonymously with destruction of avidyA. It is not to be understood that an actual production of something takes place. Also, the teachings of non-duality may also be realized from smR^iti, like the mahAbhArata, purANa-s, etc. This is made clear by sha.nkara in his sUtra bhAshhya. This is because smR^iti also teaches about topics on topics not accessible to other pramANa-s. The authority of the smR^iti comes from being derived from shruti.