Assuming you can build a laser bright enough for your detector, you are forgetting about the time & distance problem. We don’t know how far away this Planet X sits at any given point in time. You would have to pulse your laser at a spot or set of spots long enough to irradiate the possible region of space during the time it takes for Planet X to traverse said space. Then wait hours or days on the off chance the pulse comes back. If you look away too soon to examine the next spot, you miss the more distant object. If your pulse is too short, the object may pass in front or behind the pulse and be invisible.

The Sun on the other hand is irradiating all space at all times. Aside from eclipses, we know Planet X is currently reflecting sunlight. We just have to look at it, compare to background, look again, compare to background, and notice the movement.