Because the 13C spectra is one of the easiest and reliable means of identifying a molecule. The 13C gives information which complements the 1H NMR regarding Quaternary carbons, and unambiguous identification of key molecular functional groups (Aldehyde, ketone, alcohols, esters, etc.) In some cases, when the 1H NMR is ambiguous or perhaps not suitable (due to lack of protons) the 13C is the ONLY way to identify a compound.
Every new born has at least two names (first and last name) to be registered and identified, it is similar to a new molecule 1H NMR is the fisrt name and 13C is the last name and if you want to add others such X-ray, IR, UV and mass spectra, it will be easily identified
When you propose new structure several structural properties are required, many as possible in order to do an unambiguous proposal. How many instrumental techniques you need to accomplish this objective? Depends on structural complexity of your molecule. Probably you need no only 1-H and 13-C NMR spectra, but also correlation technique (NOE and DEPT). Finally, an almost-incontrovertible evidence is X-Ray Diffraction results.
Yes... 13 C spectra provide main carbon framework in the molecule, You can easily identify all the carbons like Primary secondary tertiary and Quaternary by PNDC, DEPT-135, 90 and 45.