Is fasting a precondition for the validity of i'tikaf?

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The established position is that i'tikaf is valid without fasting. This is attributed to Ali, Ibn Mas'ud, Sa'id ibn al-Musayyab, Umar ibn Abd al-Aziz, Al-Hasan, 'Ata', Tawus, Al-Shafi'i, and Ishaq. The evidence supporting this is the narration from Ibn 'Umar that 'Umar, who had vowed i'tikaf in the pre-Islamic period, was commanded by the Prophet (PBUH) to 'perform i'tikaf and fast.' If fasting were a condition, the i'tikaf for only one night would not be valid, as there is no fasting during the night. Moreover, i'tikaf is an act of worship valid at night, so fasting should not be stipulated, just as it is not stipulated for prayer.