It is not a simple filtration system. It is, as the name implies, a catalyst system.
In order to work properly, the catalyst must be maintained in the correct condition, which means, being fed the right amount of oxygen relative to fuel.
To know how much that is, the engine computer needs sensors in the cat. It then adjusts engine injection parameters to hit that number.
Without those sensors, the cat just won't work.
What is a cat doing with oxygen? Two different things. First, it wants a lack of oxygen (rich mixture) so it can reduce nitrogen oxides to nitrogen. Then it wants an excess of oxygen (lean mixture) so it can oxidize carbon, unburned hydrocarbons and carbon monoxide into CO2.
Now if you have one of those 80's cars, you have two separate catalyst beds. The engine is run intentionally rich, so the first catalyst bed can reduce nitrogen oxides. Fresh air is then injected, so the second bed can oxidize the hydrocarbons. The fresh air comes typically from a belt driven air pump.
In newer cats, they eliminate the air pump by using a cat with a heck of a trick: it stores oxygen momentarily. However, the computer must wobble the exhaust very precisely between rich and lean, in the right amount and timing to keep the cat stocked but not overwhelmed with oxygen.
It may also help the computer to know the temperature of the cat.
So that's why you need sensors on a catalytic converter.
Have your exhaust shop bolt on a plate of expanded steel mesh across the cat. The cat thief will most likely just leave and steal another car's cat. Thieves don't like variables.