It is a common practice to recite durood (greetings, blessings and salutations) on the Prophet.
The Qur'an is a guide that regulates all practices and the ethics and ideas we carry must all be based from there. If a believer feels a practice violates an ethic or a principle of the Qur'an, he or she should find the courage to adjust that practice, but not necessarily annihilate the entire practice. How does a believer have the Quranic criterion of the judgement of his practices if he does not study the Qur'an directly? One first has to understand the Qur'an in order to judge everything he sees and does:
“Have you considered those who were asked to accept judgement from Allah’s Book? When they are asked to accept judgement from Allah’s Book, some of them turn their backs and walk away!” (Qur’an 3:23)
Therefore, we first have to establish the objective of salat from the Qur'an. Allah informs us that the purpose of salat is to remember Him alone - Allah explains why salat should be observed in one of the verses:
"Verily, I am Allah. There is no god but I: So serve Me (only), and establish salah for My remembrance (وَأَقِمِ الصَّلاةَ لِذِكْرِي) ." (Qur'an 20:14)
We are to serve only Him and salah is for, as Allah says, "My remembrance (only)" - to remember Allah alone. Allah further teaches us:
"Say, 'My prayers (salah) and sacrifice, my life and death are all for Allah, Lord of all the Worlds" (Qur'an 6:162)
In addition, indirectly, in the verse:
"And the places of worship (Masjid) are for Allah (alone): So do not invoke anyone beside Allah." (Qur'an 72:18),
further emphasises this point, since masjids are places where salat is performed.
Some even use 33:56 to push their idea of sending blessings to the Prophet. One thing is constant, God's system/methodology does not change (33:62....35:43....48:23).
1 - We are told in many verses NOT to make a distinction among Allah's messengers. (3:84)
2 - Did the Prophet send blessings to him when he was alive? If not, why are we doing so? Are we following the Prophet by doing so?
Also, in terms of Salat, the Quranic command to observe the Salat for the sole reason of commemorating God is clear and unambiguous:
I am God; there is no god except Me. Therefore, you shall worship Me, and observe the Salat to commemorate Me. 20:14
Say, "My Salat, my worship practises, my life and my death, are all devoted to God, the Lord of the worlds. 6:162
Now let us first read 9:84
You shall not "tusalli ala" (support) any one of them who died, nor shall you stand at his grave. They have disbelieved in God and His messenger and died in a state of wickedness. 9:84
Every time the word Salaat is followed by the word "ala" (over) it always means "support". The words in 9:84 say "la tussalli ala" (do not support).
We can see the other examples in the Quran where the word ALA is used after the word Salat and in every case it means to support and not prayer:
God and His angels ‘Yu'salloon ala al-Nabi’ (support the prophet). O you who believe 'Salloo alayhee' (support him) and ‘Sallemoo tasleema’ (accept him wholeheartedly). 33:56
Here God and the angels "yussalloon ala al-nabi". Obviously, God does not conduct a prayer for the prophet! Rather, God and the angels support the prophet and in the same verse, we are asked to do the same (support the prophet). This ayat has been corrupted by the traditional Muslims and the result is that they go around uttering (sali ala al nabi) like parrots all day long not knowing what it really means!
The command in 33:56 was to support the prophet while he was alive, now he is dead we cannot support a dead man.
He is the One who ‘Yu'salli alaikum’ (supports you), as well as His angels, to bring you out of the darkness and into the light. 33:43
Once again, in 33:43 God supports the believers rather than conduct a prayer for them.
Take a charity from their money to cleanse and purify them with it, and ‘Salli alaihum’ (support them). Your ‘salawat’ (support) provides them with tranquility. God is Hearer, Knowledgeable. 9:103
Once again the same meaning.
Peace and blessings!