Why did the Prophet (peace be upon him) not fast the entire month of Muharram, even though it is the best fasting after Ramadan, following the example of his fasting in Sha'ban?

The best fasting after Ramadan is during Allah's month of Muharram, as Muslim transmitted. Al-Nawawi explained the Prophet's (peace be upon him) increased fasting in Sha'ban rather than Muharram by suggesting that he may have learned about the virtue of Muharram later, or that there were impediments preventing him from fasting then. However, Ibn Rajab countered that the preference for fasting in Sha'ban is like the regular Sunnah for Ramadan, whereas fasting in Muharram is superior in terms of absolute voluntary fasting. Ibn Rajab believed that fasting in Sha'ban is better than fasting in the sacred months, and that the best voluntary fasting is that which is close to Ramadan, both before and after it, akin to the regular Sunnah prayers for obligatory prayers, completing any deficiencies in the obligatory ones. Therefore, the Hadith "The best fasting after Ramadan is Muharram" is understood to refer to absolute voluntary fasting, just as the saying about prayer states that night vigil is better than absolute voluntary prayer, excluding the regular Sunnah prayers.