Wouldn't it have been easier to just covertly shadow the CIA guy and see who he meets rather than getting a Sparrow to acquaint him?
Or even easier than that, wait and see which KGB agent flies to Budapest randomly at the same time the CIA dude was in that neck of the woods?
Poor storyline, lots didn't make sense and wasn't explained well.
It would, but they risk no success, or timely no progress all the while some mole is in their nest doing all sorts of no-good.... no no, time is a luxury they do not have. Instead employ a 3 step strategy:
1 - tail him first, and see what he is up to (done before Dominika went in)
2 - put a sparrow on him to gain quicker access to any useful knowledge or hint. And if she fails move to step 3.
3 - torture the guy and drill it out of him the old fashioned way...
And this is exactly what they did.
(and btw they also used agents travel agenda to substantiate the guilty one... so that part, you agree with)