Several reasons. Outside of the reactor core itself, almost all items that “become” radioactive are just contaminated with radioactive waste. The item itself hasn’t turned radioactive, it’s just covered in radioactive particles that are usually very difficult to remove.

However, when you expose something to very high levels of neutron radiation (like you would find in a reactor core), it is possible to turn the atoms of the item itself radioactive. This is known as “activating”, and it’s how we produce many types of radiopharmaceutical drugs and other research isotopes. The amount of neutrons required to do this are basically nonexistent outside of nuclear reactors and particle accelerators, so it’s usually not a concern.

Source: my job is to put things into a nuclear reactor and turn them radioactive.