Why does Islam limit plural marriage to four wives and no more?

Firstly: 

The Muslim must submit to all the rulings of Allah, both commands and prohibitions, whether it is in accordance with his opinion or not, and whether it suits his whims and desires or otherwise. If the wisdom behind it becomes clear to him – whether the matter is prohibited or permitted – that increases him in faith and submission.

If the wisdom behind it is not clear to him, he accepts it and submits, with certainty that Allah, may He be exalted, does not prescribe anything except for a good reason, and this reason or wisdom may be hidden to some people, or some people may know some of it. 

Allah, may He be exalted, says (interpretation of the meaning):

“But no, by your Lord, they can have no Faith, until they make you (O Muhammad SAW) judge in all disputes between them, and find in themselves no resistance against your decisions, and accept (them) with full submission”

[an-Nisa’ 4:65]. 

Al-Bukhaari (321) and Muslim (335) narrated that Mu‘aadhah said: I asked ‘Aa’ishah: Why does a menstruating woman have to make up missed fasts but not missed prayers? She said: Are you a Harooriyyah (Khaariji)? I said: I am not a Harooriyyah, but I am asking. She said: That used to happen to us and we were commanded to make up the fasts but we were not commanded to make up the prayers. 

See also the answer to question no. 50330. 

Secondly: 

Plural marriage is something natural that is known in all nations, although they differ in the ways in which it is applied. When man-made laws prohibit plural marriage, people resort to having illicit relationships outside the home. Plural marriage was known during the Jaahiliyyah, then Islam came with that which is suited to sound human nature, so it put limits on what the people were doing and imposed some guidelines. 

Thirdly: 

This is a divinely ordained law, and divinely ordained law is wise in and of itself. There is no need for the accountable individual to know the reason and wisdom behind it; rather what the accountable individual is required to do is submit. 

One of the reasons behind this law is to test people. At the beginning of Islam, the qiblah (direction faced in prayer) was Bayt al-Maqdis (Jerusalem), then Allah abrogated it and commanded the people to face towards the Sacred House (the Ka‘bah, in Makkah). As for the sincere believers who were certain in their faith, they said “we hear and we obey”, but the disbelievers and hypocrites in whose hearts was doubt said: “What has turned them (Muslims) from their Qiblah (prayer direction (towards Jerusalem)) to which they were used to face in prayer?” [al-Baqarah 2:142]. 

Opening the door to argument in such matters leads to doubt concerning sharee‘ah and its rulings. Then someone will say: why are the prayers five and not six? Why is Zuhr prayer four rak‘ahs and not eight? Why is the month of Ramadan singled out for fasting to the exclusion of others? If it is said that it is because Qur’an was in that month, they may say: why was Qur’an revealed in that particular month? Why was it not revealed in a sacred month, because the sacred months are venerated? And so on, without end. The one who says “we hear and we obey” puts a stop to that altogether. 

Allah, may He be exalted, says (interpretation of the meaning): “And We made the Qiblah (prayer direction towards Jerusalem) which you used to face, only to test those who followed the Messenger (Muhammad SAW) from those who would turn on their heels (i.e. disobey the Messenger)” [al-Baqarah 2:143]. 

When the command comes, with what Allah enjoins or forbids, one should say: “we hear and we obey.” If the wisdom behind it is clear to him, or is partially clear, that increases him in faith and submission, otherwise he should continue to hear and obey, because he knows that Allah does not prescribe anything except there is great wisdom behind it. 

Allah, may He be exalted, says (interpretation of the meaning):

“The Messenger (Muhammad SAW) believes in what has been sent down to him from his Lord, and (so do) the believers. Each one believes in Allah, His Angels, His Books, and His Messengers. They say, ‘We make no distinction between one another of His Messengers’” – and they say, ‘We hear, and we obey. (We seek) Your Forgiveness, our Lord, and to You is the return (of all)’” [al-Baqarah 2:285]. 

“It is not for a believer, man or woman, when Allah and His Messenger have decreed a matter that they should have any option in their decision. And whoever disobeys Allah and His Messenger, he has indeed strayed in a plain error”

[al-Ahzaab 33:36]. 

Please see also the answer to question no. 14022. 

And Allah knows best.