In the MLB Draft, there is never much trade activity. In fact, most players selected don't get traded for a while as they work their way up the minor league system they joined on draft night. There is a reason for this: trading picks is generally prohibitted. They also legally cannot trade picked players for a while.
This year's class has two of the best prospects in recent memory: Dylan Crews and Paul Skenes. What if an MLB team, like the New York Yankees, wanted one of them? They're out of luck because they can't move up from 26th overall.
The idea behind this rule was to ensure that rich teams don't get richer. Top prospects want a lot of money. Crews wants $10 million reportedly. The Pittsburgh Pirates might not be able to afford that, so they could, in theory, trade him to the Yankees, who can afford him. This rule strives to keep competitive balance.
MLB is only league without pick trades
Whereas the MLB doesn't allow pick trading or even trading the rights to players at the draft, the NFL and NBA do. In the NFL, picks are traded all the time. Just this last draft, the Carolina Panthers traded a haul to swap from ninth overall to first.
In the NBA, it works a little differently. Teams will trade the rights to their players that they selected. For example, the Indiana Pacers selected Bilal Coubilaly seventh overall, but as a result of a trade, the Washington Wizards own his rights.