Zakat isn't a must in 6 classes of people; those who can earn their living, offspring, wives, ancestors, unbelievers, prophet's descendants, and slaves. It isn't necessary to satisfy the 8 zakat deservers.

Zakat may not be given to

1-People in money and those able to earn their living:

However, a person with sufficient means, or a rich person, may be given out of zakat if they qualify as zakat administrators or debtors. Likewise, the one who is able to earn one’s living may be given zakat money if he is studying full time, provided that he studies either Islamic studies or a discipline needed by the Muslim community. The pursuit of such studies is akin to fighting for Allah’s cause. On the other hand if a person is able to earn one’s living but does not work in order to devote his time to worship, he may not be given zakat money. Such worship is voluntary and, at best, recommended. Unlike knowledge, worship benefits the worshipper only while knowledge benefits him and others.

2-Offspring, ancestors and wives: These are relatives that a man has a duty to look after. Whatever they need for their living is his responsibility. Therefore, it is not permissible to pay one’s zakat to one’s parents, grandparents, children, grandchildren or wives. To pay zakat to them reduces his liability towards them or makes them independent. As such, he would be like one paying his zakat to himself.However, it is permissible for a wife to give her zakat to her husband if he is poor, needy or in debt he can't pay off.

3-Unbelievers who do not belong to those whose hearts are to be won over: It is not permissible to pay zakat to unbelievers,

The Prophet was referring to the rich among the Muslims and their poor. One of the main objectives of zakat is to make those Muslims who are poor self-sufficient, and to strengthen the ties of love and brotherhood within the Muslim community. 

4-The Prophet’s (peace be upon him) descendents: Zakat may not be paid to the Prophet’s (peace be upon him) descendents. This is out of respect to the Prophet and his household and because they have a portion to be paid to them from the spoils of war as mentioned in 8:41 “And know that anything you obtain of the spoils of war – then indeed, for Allah is one fifth of it and for the Messenger and for [his] near relatives and the orphans, the needy, and the [stranded] traveler”.The Prophet (peace be upon him) says:

Members of the Prophet’s (peace be upon him) household are said by some scholars to be the descendants of the clans of Hashim and al-Muttalib. Other scholars limit them to the Hashim clan, which means that zakat may be paid to the descendants of the al-Muttalib clan. This is the weightier view. 

5-The slaves freed by members of the Prophet’s (peace be upon him) household: 

6-Slaves: Zakat may not be paid to a slave, except one who has made an agreement with his master to buy his own freedom. He is paid zakat money to help him pay for his freedom.

It is not necessary to satisfy all eight classes of beneficiaries when distributing the zakat funds. It is perfectly permissible to pay all the zakat funds to one only of these classes.

As we have noted, the Prophet (peace be upon him) defined zakat as a donation ‘to be taken from the rich among them and given to their poor.’ Moreover, Qabisah ibn Mukhariq undertook to pay the costs of sorting out a dispute between some of his people. He went to the Prophet (peace be upon him) to request help in this payment.