Tbh you have to ask what is even a secret police? It’s, supposedly, people in a police force (i.e. a tool of repression from the state) that don’t identify themselves as such, for example by wearing

By that definition when you come across an undercover cop, they’re secret police. When the cop has left work and changed into their civilian clothes and you wait in line with them at the store, they’re secret police. When the feds want to ask you some question and don’t identify themselves (but you still have to obey because they’re still cops), they’re secret police.

“Secret police” is one of those words that sounds scary but it means nothing in practice. Under Lenin the Soviets started the NKVD who was military police. The NKVD investigated military matters, and during the revolution they also investigated into the enemies of the army, as it was a military matter too. For example if an enemy soldier surrenders, then it makes sense to turn them over to the military police for questioning.

Why? Perhaps being invaded by external armies and spies made their mind about it.

The full name of the secret police gives you a hint:
“All-Russian Extraordinary (or Emergency) Commission for Combating Counter-Revolution and Sabotage under the Council of People’s Commissars of the RSFSR”

What CriticalResist said is most relevant, so as to not repeat what they said, I’ll try to go at this from a slightly different angle.

Before we ask “why does this country have ‘secret’ police” we first have to ask why they have police in the first place. The answer to that, almost always, is the enforcement of laws and the upholding of the values of the state. Even in so-called ‘Libertarian’ examples, the police are utilized for those two things. However, in those examples, it’s usually either militias or people’s movements that act as the police.

Now having established why the police exist, why would a state need special forces or more task-oriented law enforcement departments? To put it simplistically, military police, police special forces, detective agencies, etcetera exist because the average police officer is simply incapable of larger scale or speciality law enforcement. The KGB existed for a few core reasons, but at its heart, the KGB’s existence was necessitated by the existence of the CIA in the US, or MI6 in England. The KGB, or ‘Komitet Gosudarstvennoy Bezopasnosti’ (Committee for State Security) acted in the motherland primarily for defence against foreign instigators. Namely agitators from the United States and Western Germany. They also did some limited border patrolling and high-level law enforcement. They differed from the NKVD in that they didn’t only tackle military investigations, but civilian ones too, as well they acted exterior to the USSR’s official borders.

The USSR utilized the NKVD and the KGB to protect the motherland and the interior from external threats, entirely because they were forced to by those external threats.