Why is being an unregistered animagus against the law?

Question

The wizarding world also has invisibility cloaks, disillusionment charms and polyjuice potions - using those a wizard can also disguise himself. All of those seem legal. An unregistered animagus, however, faces a sentence in Azkaban. Why is there a law against unregistered animagi at all?

Answer 1

Animagi are most commonly used by those involved in espionage and crime

Animagi make up a small fraction of the wizarding population. Achieving perfect, spontaneous human to animal transformation requires much study and practice, and many witches and wizards consider that their time might be better employed in other ways. Certainly, the application of such a talent is limited unless one has a great need of disguise or concealment. It is for this reason that the Ministry of Magic has insisted upon a register of Animagi, for there can be no doubt that this kind of magic is of greatest use to those engaged in surreptitious, covert or even criminal activity.
_{The Tales of Beedle the Bard - Albus Dumbledore on "Babbitty Rabbitty and her Cackling Stump"}

There is nothing "illegal" about becoming an Animagus. It's just a very difficult and time consuming skill for one to learn, and the only people who can afford to spend the time are usually the people who are will be using it often. These are the types of people that the ministry would want registered.

An Animagus has a great potential advantage in the spheres of espionage and crime. For this reason, an Animagus Registry exists on which all Animagi are expected to log their personal details and the precise appearance of their transformed self. It is usually the case that distinctive markings or disabilities belonging to the human body will transfer to the animal self. Failure to enter oneself onto the Registry may result in a stretch in Azkaban.
_{Pottermore - Animagi (behind paywall)}

Invisibility cloaks, disillusionment charms, and polyjuice potions are all things that any witch or wizard can employ. There would be no purpose in having a registry of everyone who is Polyjuice-capable as everyone is. In contrast, only 0.1% of wizards are Animagi.

It is immensely difficult to change oneself into an Animagus and the process, which is complex and time-consuming, can go dramatically wrong. As a result, it is believed that fewer than one in a thousand witches or wizards are Animagi.
_{Pottermore - Animagi (behind paywall)}

Of course, an Animagus is also a much more useful form of disguise, as it doesn't require any tools, and lasts indefinitely.

One last point to be aware of is that while Animagi, Polyjuice Potion, Invisibility cloaks, and the like may be legal, breaking the law with them is not.