Why do we send blessings upon the Prophet and his family in the prayer and not upon the rest of the ummah?

Praise
be to Allah

Firstly:

Submission to Allah and His Messenger is one of the
fundamentals of the Islamic religion, without which it cannot be complete.
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 (blessings and peace of Allah
be upon him)) 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].

Submission leaves no room for doubt and it puts an end to the
whispers of the Shaytaan. By means of submission one may attain certainty
and perfect faith, and when there is submission, one does not need to ask
why or how.

Secondly:

People are all equal in terms of them being slaves of Allah,
but after that they very in status and virtue according to their level of
piety or fear of Allah, as Allah, may He be glorified and exalted, says
(interpretation of the meaning):

“O mankind! We have created you
from a male and a female, and made you into nations and tribes, that you may
know one another. Verily, the most honourable of you with Allâh is that
(believer) who has At-Taqwa [i.e. he is one of the Muttaqoon (pious)]”

[al-Hujuraat 49:13].

The Messenger of Allah (blessings and peace of Allah be upon
him) said on the middle day of the days of at-Tashreeq: “O people, verily
your Lord is one and your father is one. Verily there is no superiority of
an Arab over a non-Arab or of a non-Arab over an Arab, or of a red man over
a black man, or of a black man over a red man, except in terms of piety.
Have I conveyed the message?” They said: The Messenger of Allah (blessings
and peace of Allah be upon him) has conveyed the message.

Narrated by Ahmad (22978) and classed as saheeh by al-Albaani
in as-Saheehah (2700).

Thirdly:

Sending greetings of salaam upon the Prophet (blessings and
peace of Allah be upon him) and upon the righteous slaves of Allah in the
prayer is done in the tashahhud, which is then followed by sending blessings
upon the Prophet (blessings and peace of Allah be upon him) and upon his
family.

The greeting of salaam is sent upon all the righteous slaves
of Allah in heaven and on earth, as al-Bukhaari (831) and Muslim (402)
narrated that Ibn Mas‘ood said: When we prayed behind the Messenger of Allah
(blessings and peace of Allah be upon him), we used to say: Peace (salaam)
be upon Allah, peace be upon So and so. The Messenger of Allah (blessings
and peace of Allah be upon him) said to us one day: “Allah is as-Salaam, so
when one of you sits to pray, let him say:
at-Tahiyyaatu Lillaahi wa’s-salawaatu wa’t-tayyibaat; as-salaamu ‘alayka
ayyuha’n-nabiyyu wa rahmat-Allahi wa barakaatuhu; as-salaamu ‘alayna wa ‘ala
‘ibaad-illaah is-saaliheen (All compliments, prayers and good words are
due to Allah; peace be upon you, O Prophet, and the mercy of Allah and His
blessings; peace be upon us and upon the righteous slaves of Allah). For if
you say that it will reach every righteous slave in the heavens and on
earth. (Then say:) Ash-hadu al-laa ilaaha ill-Allah wa ash-hadu anna
Muhammadan ‘abduhu wa rasooluhu (I bear witness that there is no god
except Allah and I bear witness that Muhammad is His slave and Messenger).”

As for sending blessings when saying “Allahumma salli ‘ala
Muhammad… wa baarik ‘ala Muhammad” what is prescribed is for it to be
intended for the Prophet (blessings and peace of Allah be upon him) and his
family, and it is said after the Tashahhud.

This is how it is prescribed and it is prescribed to be
exclusively for the Prophet (blessings and peace of Allah be upon him) and
his family. Allah instructed His Prophet (blessings and peace of Allah be
upon him) to say it this way, and He has commanded people to follow the
Prophet’s example and act in accordance with his Sunnah, as the Prophet
(blessings and peace of Allah be upon him) told us when he said: “Pray as
you have seen me praying.” Narrated by al-Bukhaari (631).

Allah, may He be exalted, bestows His favour and generosity
upon whomever He will among His slaves. He is not to be questioned about
what He does and no objection is to be raised to what He prescribes on the
basis of what people may think or imagine. Allah, may He be exalted, says
(interpretation of the meaning):

“He selects for His Mercy (Islam
and the Qur’an with Prophethood) whom He wills and Allah is the Owner of
Great Bounty”

[Aal ‘Imraan 3:74]

“That is the Grace of Allah which He bestows on whom He
wills. And Allah is All-Sufficient for His creatures’ needs, All-Knower”

[al-Maa’idah 5:54].

It is well-known that the family of the Prophet (blessings
and peace of Allah be upon him) enjoy special virtue and status that others
do not share.

Moreover, the grace of Allah will be bestowed upon the
righteous and His slaves with the sending of greetings of salaam upon them,
as we see above. Obviously, it is not necessarily the case that those who
are favoured receive equal favour in all things.

Our Prophet (blessings and peace of Allah be upon him) taught
his Companions to send blessings upon him when they said to him: O Messenger
of Allah, we know how to send greetings of salaam upon you, but how should
we send blessings upon you? He said: “Say:
Allahumma salli ‘ala Muhammadin wa ‘ala aali Muhammadin kama salayta ‘ala
aali Ibraaheem, innaka hameedun majeed; Allahumma baarik ‘ala Muhammadin wa
‘ala aali Muhammadin kama baarakta ‘ala aali Ibraaheem, innaka hameedun
majeed (O Allah, send Your salaah (grace, honour and mercy) upon
Muhammad and upon the family of Muhammad, as You sent Your salaah
upon the family of Ibraaheem, You are indeed Praiseworthy, Most Glorious. O
Allah, send Your blessings upon Muhammad and the family of Muhammad, as You
sent Your blessings upon the family of Ibraaheem, You are indeed
Praiseworthy, Most Glorious).”

Narrated by
al-Bukhaari (6357) and Muslim (406).

This is how
to send blessings upon him (blessings and peace of Allah be upon him), and
not one of them said: O Messenger of Allah, why do we send blessings upon
you and upon your family, and we do not send blessings upon the Prophets and
Messengers of Allah, or upon any of your Companions or any of your ummah?
They only said, as Allah tells us about them and about His believing slaves:
We hear and we obey. This is what is required of us.

Fourthly:

What is meant
by the family of the Prophet (blessings and peace of Allah be upon him) is
his wives and descendants, and Banu Haashim and Banu’l-Muttalib.

See also the
answer to question no. 10055.

And Allah
knows best.