Why Does Mohammed Need Peace Upon Him?

Good Muslims, whenever they say the name of Mohammed or any other prophet, will then say, "alayhi as-salām", which is usually translated as "may peace be upon him".  But why, as Islam's greatest and final prophet, would Mohammed now be in any need of peace?

Ignore, for a moment, the Bible's teaching that our eternal destiny is fixed by our choices in this life, and that no prayers or blessings for us will help us in any way after we are dead.

the death of Muhammed,
from a 16th century Turkish epic

Also ignore for now the argument by some Christians that "alayhi as-salām"  is more accurately translated "the prayers of Allah be upon him and peace" (which raises another whole conundrum, but still leaves us with peace being invoked upon Muhammed).  

I could understand if his followers said this while he was alive.  I could understand if the blessing today was something like "may honor be upon him" or "may his teachings be followed" or even "may peace be upon his followers".  But... today to say, may peace be upon him?  Why isn't this seen as insulting to Mohammed?  If a non-Muslim were to suggest publicly that Mohammed lacks peace because he is burning in hell right now, there would probably be violent protests by some Muslims (think Danish cartoons).  But (unless I am missing something here), hundreds of millions of times a day, Muslims suggest this very thing by blessing their prophet with peace. 

Why would they follow a prophet whose followers must pray he experiences peace, after his death?

Why not instead follow a Prophet who blesses His followers with peace?

"Peace I leave with you; My peace I give to you; not as the world gives do I give to you. Do not let your heart be troubled, nor let it be fearful. [Jhn 14:27 NASB]

"These things I have spoken to you, so that in Me you may have peace. In the world you have tribulation, but take courage; I have overcome the world." [Jhn 16:33 NASB]

So when it was evening on that day, the first day of the week, and when the doors were shut where the disciples were, for fear of the Jews, Jesus came and stood in their midst and said to them, "Peace be with you." ... So Jesus said to them again, "Peace be with you; as the Father has sent Me, I also send you." ... After eight days His disciples were again inside, and Thomas with them. Jesus came, the doors having been shut, and stood in their midst and said, "Peace be with you." [Jhn 20:19, 21, 26 NASB]

Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ, [Rom 5:1 NASB]

Grace to you and peace from God our Father and the Lord Jesus Christ. [1Co 1:3 NASB]