The Matrix vs The Matrix Sequels

[NEM0]

I always kind of got the feeling that Agents would only notice a redpill when a bluepill saw an event that surprised them, and made them somewhat aware of the false nature of The Matrix. They see something they know to not be possible, so they start to become aware that the world around them has problems, and doesn't seem real. For example, the hobo in the train station wasn't taken over by Smith immediately, it was only until he saw Morpheus jack out. In that sense, the Machines could monitor the bluepills for surprise or a partial awakening. You could argue that the story required Morpheus and Trinity to jack out before Smith arrived, setting up Smith's fight with Neo, but I'd like to believe otherwise lol.

As far as why did Agents not just take over Neo, I think after you begin to awaken, you're somewhat disconnected from the system. After you begin to realize there is something wrong with The Matrix, they lose a certain level of control. That's why they are forced to chase down potential redpills instead of just inhabiting them.