It overlooks one important point. Jesus knew things about the situation that could have only come by special revelation. He knew, for example, the purpose behind the sickness and death of Lazarus
4 When Jesus heard that, He said, This sickness is not unto death, but for the glory of God, that the Son of God may be glorified through it.
And He knew that Lazarus had already died by the time the message reached Him, something His disciples did not know and something that He could not have known except by revelation.
11 These things He said, and after that He said to them, Our friend Lazarus sleeps, but I go that I may wake him up. 12 Then His disciples said, Lord, if he sleeps he will get well. 13 However, Jesus spoke of his death, but they thought that He was speaking about taking rest in sleep.
So, is too much for you to believe that Jesus already knew Lazarus was sick unto death way before first word of his illness ever arrived and that Jesus presence to heal Lazarus would be needed and sent to Him? In fact, Jesus knew about the coming request long before the request ever arrived!! Didnt He say that the Father knows what we have need of even before we ask Him (Matt. 6.8)and that the Father loves the Son, and shows Him all things that He Himself does (John 5.20)?
Apparently, Jesus did not have to be in Bethany to be well aware of what was happening in Bethany.
And Jesus did not have to be in Bethany to heal Lazarus. He was quite adept at healing long distance (remember the Centurions sservant and the Noblemans son?)
Fact: Jesus knows we are going to ask before we ask. He even knows when we are going to be sick before we get sick. He even knows when we are going to die before we die.
Fact: Jesus knew all along that Lazarus was sick, that word would be sent to Him requesting His presence to heal his sick friend, that He would refuse to respond by waiting two more days, that Lazarus would succumb and die from the illness and that a great object lesson concerning the resurrection of the body would take place.
Fact: Had Jesus wanted to He would have already been in Bethany the moment Lazarus got sick so the request would not have taken so long to reach Him. He didnt because He did not intend to answer the prayer for healing. He chose, instead, to allow Lazarus to die of the illness.