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One of the embedded assumptions I seem to see in discussions about this object is that objects like it (from outside the solar system) are rare.

Is this truly the case, or is it just hard to monitor the paths of the multitude of objects passing by earth?

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It is rare because other systems that form these objects are VERY far away (trillions of KMs). Imagine trying to slide a hockey puck from one end of a hockey rink to the other, but have it pass through a small (~1M) circle at the far end from you. If you took 1000 attempts even randomly, you'd probably hit the circle by accident at some point. Now someone else is also shooting at the circle, but they are 50,000KM away. Suffice to say no matter how many attempts that person takes, it will be significantly more rare to see their puck cross through the circle than yours.

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