The most controversial issues of all tend to be the ones that many people wish to see implemented uniformly across the nation. When the central government cannot accept the individual wishes of states and vice versa, conflicts form. One of the best examples of this is the American Civil War. Leading up to the American Civil War, America split into two opposing factions over slavery. The inability of the states and central government to come to an agreement was one of the factors which led to the Civil War. 
In more recent times in the US, issue such as mask-wearing to prevent the spread of Covid-19, and abortion have created a huge struggle between states and the central government, with many people believing the central government most impose rules on individual states.
The central governments often get into fights with their member states.
In the US the conflict between different groups over how power should be devolved has been constant, stretching back to the founding fathers. More recently the New Federalist movement in the 20th Century, led by Ronald Regan, objected to Roosevelt's New Deal for undermining some state rights.
Historically, federalism has not prevented conflict and has even caused it. Few can agree on what powers should be devolved to who and to what extent. Many people see a need to dictate major controversial or moral issues from the center.