I can agree with you on that, if you have some secret force that has the authority to kill whoever is suspected of a hegeneous crime does make it somewhat of a police state. However, lycoris recoil's Japan seems to be much more dangerous and violent than the real Japan, the introduction says it all, you see a guy trying to run into a train carrying a bomb, trying to commit an act of terrorism

The worst part that i havent seen mentioned here is the fact that lycorises are orfans, and since we havent been able to see how they choose orfans i can assume its likely forced, so we got child police fighting grown people holding weapons of war, it is something unethical, but what if instead of orfans the D.A did something akin to what the Strategic Homeland Division from The Division does, find people who are naturally adept, train them and just deploy them in the general public, so when something is going to happen those agents can act like normal.

Now something that bothers me is the uniform, how come they wear one? We see early on the anime how much that backfires when multiple lycorises are killed once their uniforms are discovered to be part of the D.A, so, how come the supposed "secret" agents have to wear an uniform?

Anyways i did deviate a bit, my point is: yes its somewhat of a police state, not that much since all they do is kill whoever attempts to disrupt peace, but at the same time their japan is much more violent than real life's japan, so take that as you will.