Another wrinkle occurs when there is another house that needs to be sold to procure your new house, and/or the house in which you're buying is not vacant prior to your purchase. A minor delay in either transaction also impacts the sale of your home. So your movers, house cleaners, packers, and the like need have to have some flexibility built into their schedules such that moves can be made efficiently and smoothly.
It's also not uncommon for home buyers and sellers to "have to" move on a particular date or the sky will fall. But when an issue then crops up on their end (for example their loan docs are late), miraculously they find a solution! Often, buyers want to move some of their belongings into their new home either prior to close and/or after closing but prior to their contractual date of possession (often 3 days after close of escrow). Never a good idea! Whose insurance covers those belongings, and what about the person moving out of the property -- their life is generally in a state of mild chaos as well, and the added stress of others moving items around them generally isn't good for anyone involved -- that's why mini-storage exists! Rent a unit for a month, and use it as a buffer in the event of delays in your closing date. Or rent a pod and see if you can negotiate having it delivered to the driveway (as long as it doesn't block access) of the new house after closing --but before you're allowed possession -- that seems like a reasonable compromise and you won't have to move twice! Be prepared to stay in a hotel for a few days if necessary as well -- preferably one with a spa so that you can relax a little during this hectic time!