In regards to the question of freedom of speech (SEP), limits are almost universally accepted by social institutions responsible for maintaining order through the use of the law. What those limits are very greatly from culture to culture depending on the consensus on what constitutes 'law', 'speech', and 'morality'. It's not possible here to answer in regards to all philosophical traditions since there is no consensus on what these things are, so there is not consensus on what the limits are. But it is possible to select one tradition, that of English common law, and use it as an example. Broad notions of freedom of speech are generally adopted by political philosophies that are seen as liberal, and liberalism has a series of philosophical beliefs that leaders, elected or otherwise, are not above the law of the land.
Let's start with the English tradition and cite SEP's article "Freedom of Speech" regarding John Stuart Mill, a seminal figure, along with Edmund Burke in English political philosophy:
Given that Mill presented one of the first, and still perhaps the most famous liberal defense of free speech, I will focus on his arguments in this essay and use them as a springboard for a more general discussion of free expression. In the footnote at the beginning of Chapter II of On Liberty, Mill makes a very bold statement:
If the arguments of the present chapter are of any validity, there ought to exist the fullest liberty of professing and discussing, as a matter of ethical conviction, any doctrine, however immoral it may be considered. (1978, 15)
This is a very strong defense of free speech; Mill tells us that any doctrine should be allowed the light of day no matter how immoral it may seem to everyone else.
From here, we can make plain what you talk about when you talk about the primacy of the right to free speech.
Since there are vast differences between ideas about freedoms and rights in the Anglo-American common law, Continental law, and Sharia law, among, others, we'll show how even under the most liberal philosophies, limits need to be set to avoid anarchy and harm.
One work that was important in the Anglo-American tradition within which Mill operated was his On Liberty which argued that the freedom of speech wasn't a natural right, but rather a result of utilitarian thinking. According to WP:
[Mill argued] a person should be left as free to pursue his own interests as long as this does not harm the interests of others.
And according to IEP's article on John Stuart Mill:
On Liberty puts forward the “harm principle” that “the only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others.”
So, do concepts about limits to freedoms, particularly speech apply to leaders? Absolutely, and this was put into writing in England as the Magna Carta all the way back in 1215! And as common law evolved, the people, who were mainly land-holding nobles, gained more and more rights that were previously the privilege of the monarchy. Modern political scientists talk about legal restrictions on the freedom of rules in the context of constitutional monarchies. Another noted document in the constraint of the rights of leaders came in the form of the US Constitution, the second government of the American colonies of England. Prior to the American Revolutionary War, there were claimed abuses under King George III who may have picked up some authoritarian tendencies from his royal, German forefathers. In an age when monarchies were the norm, and those monarchs had tremendous freedoms and power, the American colonies opted with three co-equal branches of government and called for a non-royal executive, the President, to be elected by the legislature, the Congress part of which had powers of quasicriminal impeachment and a judicial system which eventually was recognized as a mechanism for judicial review. This was an attempt to set the leaders in the nation responsible for policing themselves, and is known as separation of powers.
But ultimately, the rights of leaders in the West, in the modern era ultimately are constrained by the electorate. Thus, the freedom of speech of evil leaders is not proscribed so much as discouraged by the electoral power those leaders cite as their legitimacy.
In the US and the UK, it is widely claimed that no one is above the law, though obvious abuses of power are many and easy to cite. One recent example is after hundreds of years of a peaceful transition of power, the 45th President of the United States, has been accused of inciting a small, ineffective attack on the US Capitol on January 6, 2021, home to Congress, in an attempt to overturn the election that certified Joseph Biden, the sitting President of the United States. It remains to be seen if this unprecedented attempt to undermine an election is the first and only, an aberration, and which leaders will be held responsible, if any, for fomenting mob action that undeniably led to the deaths of several people while the Vice President was whisked away and protected from those out to harm him.
One particular branch of legal tradition, common law, which is the basis of law in the US and the UK as well as many former colonies of the British Empire, does have related philosophies, such as Conservatism and Liberalism, that have very specific views on constraining the rights and actions of leaders. In these places, there has been an emphasis on peaceful transitions of power, and leaders, though they have the right to use speech irresponsibly, have often found themselves constrained by political realities and have exercised caution in accordance with their representative democracies. It is these philosophies that have been most successful at eliminating political corruption and malfeasance in office.