Shaykh Ul Islam Imam Muhammad Anwaarullah Farooqui (May Allah sanctify his secret) - Life and teachings

Hadhrat Shaykh Ul Islam answers to the logic-based arguments on this in a beautiful manner:

Translation: Now the talk that among philosophers, it is not considered valid that the Holy Prophet (Sallallahu alaihi wa sallam) can pay attention to each and every person at the same time, then this discussion is for some other time.  With such thoughts, the philosophers have suspended the Powers of the Lord Almighty also and have clearly and explicitly said that Almighty Allah does not know the details of His creation.  But Muslims consider such thoughts to be whisperings from Satan.  They know that Almighty Allah is attentive towards every grain of sand present in universe and that He can give the Holy Prophet (Sallallahu alaihi wa sallam) such power when some follower (Ummati) of His calls out to Him, He (Sallallahu alaihi wa sallam) directs His attention to that Ummati and can direct His attention towards all of them also at the same time.  If this were impossible, then Almighty Allah would never have allowed the Holy Prophet (Sallallahu alaihi wa sallam) to order all Muslims to say and ask for His attention:

“Assalamalaika Ayyuhan Nabiyyu”

This shows that we ask, we request the Holy Prophet (Sallallahu alaihi wa sallam) that as per command, we present ourselves at the door of the Almighty, but neither do we have the ability to present ourselves to Him nor is our worship of such standard that the Lord may accept it.  Your help is required that this worship, this supplication reaches the door of acceptance.  In the same way, the Companions, the Tabi’en would call out to the Holy Prophet (Sallallahu alaihi wa sallam) in times of need as they knew that the Holy Prophet (Sallallahu alaihi wa sallam) is given power over this universe.” (Maqaasid ul Islam Vol. 10, Pg No: 98, 99)