It is true, the removal of nasal packing after an operation was painful, not least because of the way it used to be performed. Nasal tampons were inserted essentially for two reasons:
to maintain the central position of the nasal septum at least until definitively stabilized by cicatricial (scarring) fibrosis.
to prevent the hemorrhages that could take place from the septum or the turbinates.

It must also be recognized that haematoma of the nasal septum, which consists in the collection of blood inside the septum between its two walls of mucous, can have very serious consequences, including severely damage to the external shape of the nose.
The nose was therefore packed with gauze tampons that were removed after 4–5 days or even longer by some surgeons. The gauze dries out during this period and its removal can be painful.
It can be stated that today tampons are only necessary in very particular cases.
The septum can in fact be held in place without using tampons but rather internal sutures that are eliminated by themselves with no disturbance for the patient. The turbinates are also treated when necessary by means of radio frequencies or other "soft" techniques that avoid bleeding and therefore do not require tampons.
As a result of these techniques, nasal tampons are used today in less of 5% of rhinoplasties* and are in fact employed only in cases involving major reconstruction of the nasal septum.

*Data drawn from personal records of the last 200 operations performed (at November 30th, 2011):
nasal packing in 4.7% of cases including all rhinoplasties and rhinoseptoplasties;
nasal packing in 0% of cases including only purely aesthetic rhinoplasties.