There is some problem. Do you think?
What happens when size of blockchain becomes a giant value?
If synchronisation have already takes about 40 minutes then what'll happen after many years of life of the coin.
Initial Bitcoin-qt synchronization can take more than one day. It's about 20GB of data.
But there are other solutions, read about SPV.
https://en.bitcoin.it/wiki/Thin_Client_Security#Header-Only_Clients