Solid handoffs on 4X100m relays require great timing and chemistry between athletes. If you examine some of the top high school and collegiate relay teams, it usually involves a group of four athletes who compete on the same relay team all season, sometimes in the same order every race. After running with teammates over and over, they figure out all the variables, like when and where in the exchange zone they are comfortable passing, how quickly the outgoing runner accelerates, how high their hand will be when they reach back to receive the baton, how to react in the event of a bad pass, etc. It's all things learned through repetition.
Professional relay teams are groups of athletes who do not have the repetition. It's rare that they have trained or competed together before joining the team. In a few instances, many of the athletes who end up on a national or Olympic team have never even met before gaining an invite to the relay. They're basically a group of strangers running together. Granted, these strangers usually have a lot of experience running relays, but they just don't have experience running with each other.
Another big difference between pro relay teams and lower level teams is the speed. Because elite athletes are so fast, the margin for error is tiny. A small mistake can lead to defeat. If a high school relay team has a mistimed or messy handoff, they can still recover and win a race. If a pro team makes that kind of error, the race is over for them. Because there is no room for error, they have a "go for broke" attitude: go gold or go home with nothing. This leads to the dropped batons.