OF COURSE we want moshiach to come!! Why wouldn’t me – who by the mid 20’s hasn’t felt suffering, stress, pain, loss of a loved one… and today?? who hasn’t felt the pain of lieby kleitzy, the suffering in israel, mumbai attack…. the list can go on and on and on… we would be crazy not to want moshiach.
And yes we want to be closer to Hashem but I think mainly what people think of when they say they want moshiach is for all the suffering to end…