Bringing down stable governments of countries and failing to put something in its place is the principal cause of the terrorism and conflict going on in the world at the moment.
When the Romans invaded, they took control, dictating foreign policy, providing defence in exchange for a promise to not rebel and pay tribune. In so doing peace reigned over the Roman Empire at the cost of freedoms at a national level. This was the pax Romana.
The Islamic Golden Age, inspired by the philosophy that “the ink of a scholar is more holy than the blood of a martyr“, in which huge advances were made in medicine, mathematics, culture and science, was also a period of peace, sometimes called the pax Islamica.
A thousand years later the Mongols conquered much of Asia and held it to produce the Pax Mongolica.
The Ottoman Empire in turn provided peace to its citizens in the pax Ottomana.
A similar arrangement to the Roman Empire was achieved by the British Empire to produce the pax Britanicca.
Chinese empires have come and gone and provided their own periods of internal peace, as have many other cultures.
The concept of “empire” has come to be seen as purely a bad thing since the mid 20th century as countries gained their independence, partly through economic consequences of the World War 2, partly through improved communication and education and partly through the disruptive influences of the Cold War. In place of an imposed external governing body, freedom for those of a territory has been granted, often with disastrous consequences. The lesson that could and should have been learned from those experiences are that independence should be done slowly, replacing institutions and structures with new ones, a part at a time. It is frustrating, but far more stable. [Note to self: specific examples needed.] A clean break leaves a county with no stable government and civil war and decades of turmoil is the usual result.
But the desire to ignore the beneficial benefits of a benign empire has resulted in much chaos, death, suffering and desire for revenge of late years. The removal of stable governments from countries like Iraq and Libya without replacing it with something else that works has been far worse than what most empires have done in the past.
It would have been cheaper and less destructive (but probably no more productive in the long term) to simply assassinate those leaders that were considered undesirable. At least there would not be hundreds of thousands of dead and maimed civilians and a world-wide problem with revenge terrorism.
The idea the USA has been the global policeman producing a pax Americana is a fallacy. They are not spreading peace: just fear and hate, chaos and disorder.
Instead of toppling a regime, take it over and change it from within, fools. Learn from thousands of years of history.