What is meant by istimta in the verse "فما استمتعتم به منهّن فاتوهن اجورهنّ فریضة"; (For the enjoyment you have had from them thereby, give them their dowries, by way of settlement) , is intimacy and taking pleasure, so the verse is saying: Whenever you have taken pleasure in women provide them with their mahr (dowry).
The Shiite and also a group of scholars from the Sunni school of thought maintain: The verse implies the religious ritual of temporary marriage.
Muslim Ibn-Hajjaj has narrated in a sahih (auhtentic) hadith that Ata said: Jabir Ibn-Abdullah had recently arrived from Hajj and we went to visit him.
The people asked him about several issues one of which was mut'ah (fixed-term marriage). He replied: "Yes, we practiced mut'ah in the time of the Prophet, Abu Bakr and Umar."
Thus we can understand why the great figures of the Sahabah (Companions of the Prophet) and the Tabe'in (Followers; Muslims born after the Prophet, but contemporaries of the Sahabah), a large amount of Sunni mufassirs (interpreters of the Quran) and all Shiite mufassirs have understood mut'ah from this verse.
The verse is seeking to mention those women who are legitimate to marry, instead of demanding to partake in the ritual of temporary or permanent marriage. Essentially, marriage, temporary or permanent, isn't wajib per se, but rather it is mustahabb (recommended)[i] hence there is no reason for the amr (imperative) form of the verb regarding this topic. So regarding the second part of the question the answer is that the primary implication of an amr (imperative) form of a verb in Fiqh (Islamic jurisprudence) is wujub (obligation) but no one has claimed temporary marriage to be wajib (obligatory).
[i] Fazel Lankarani, Mohammad, Tafsil Al-Shariah fi Sharh Tahrir Al-Wasilah, chapter of nikah, pg. 7.
Detailed Answer
Philologists state that the term istimta' means intimacy and taking pleasure, so the verse is saying: Whenever you have taken pleasure in women provide them with their mahr (dowry).
Ibn Abbas, Sada, Ibn Sa'id and a group of the Tabe'in (Followers; Muslims born after the Prophet, but contemporaries of the Sahabah (Companions of the Prophet)) and The Followers of the Ahlul Bayt maintain: What is meant is temporary marriage.
This issue is pretty clear and evident, for although the term "istimta" and "tamatu'" literally mean taking pleasure and benefit, and in shar'i terms, this is confined to this type of contract , especially when it is combined with women (for example when it is said taking pleasure in women).
Therefore the meaning of this verse would be: "Whenever you have performed temporary marriage with them, give them their dowries".
It has been narrated by a group of the Sahabah (Companions) namely Ubayy bin Ka'b, Abdullah Ibn Abbas and Abdullah bin Masuud that they used to recite this same verse in a slightly different way: "فما استمتعتم به منهن الى اجل مسمّى فآتوهن اجورهن"; meaning that whenever you take pleasure in them for a fixed term, give them their dowries from which clearly temporary marriage can be understood. This is very explicit and direct in mut'ah and temporary marriage.
Hence we can understand why the great figures of the "Sahabah" and "Tabe'in"; such as Ibn Abbas, the great scholar and renowned interpreter of the Quran, Ibn Ka'ab, Jabir Ibn Abdullah, Amran Husein, Sa'id Ibn Jubair, Mujahid, Qutadah, Sada, a vast majority of Sunni Interpreters and every single Shiite interpreter have understood the subject of mut'ah (fixed-term marraige) from the aforesaid verse to the extent that Fakhr Razi, who is known for being a tough critic of Shia standpoints, after thoroughly studying and discussing the verse, states: "We don't deny the fact that the verse pertains to temporary marriage, what we are saying is that the hukm [of mut'ah] has been revoked later after its revelation."[1]
Now regarding the second part of your question as to why Allah didn't demand his Prophet to perform temporary marriage and why the Prophet wasn't addressed in the amr (imperative) form of the verb for istimta', we must say:
The primary implication of the amr (imperative) form of a verb is wujub (obligation) and nobody has claimed temporary marriage to be wajib (obligatory).[2]
Accordingly, the verse is seeking to mention those women who are legitimate to marry, instead of demanding to partake in the ritual of temporary or permanent marriage itself. Essentially, marriage, temporary or permanent, isn't wajib per se, but rather it is mustahabb (recommended),[3] hence there is no need for the amr (imperative) form of the verb regarding this topic. On the other hand ahkam (Islamic rulings) are for everyone, not exclusively the Prophet (S.A.W.). As a result, if a verse in the Quran is pronouncing a taklif (religious duty) it will apply to everyone and they must to abide by it, even if the verse is only addressing the prophet.
[1] Makarem Shirazi, Naser, Tafsir Nemouneh, vol. 3, pg. 336.
[2] It should be noted that in the case of many wajib rulings we have that everyone agree on, their respective verses or hadiths don't employ imperative verbs; for example, the obligation of fast; Allah (swt) says: "O you who have faith! Prescribed for you is fasting as it was prescribed for those who were before you, so that you may be God wary" (Baqarah:183), or the obligation of performing Hajj; Allah says: "In it are manifest signs [and] Abraham's Station, and whoever enters it shall be secure. And it is the duty of mankind toward Allah to make pilgrimage to the House for those who can afford the journey to it and should anyone renege [on his obligation], Allah is indeed without need of the creatures." (Ale Imran:97).
[3] Fazel Lankarani, Mohammad, Tafsil Al-Shariah fi Sharh Tahrir Al-Wasilah, chapter of nikah, pg. 7.
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