None of that involve pretending he has any chance romantically.
The downfall of her family isn't a mystery at all, we know how and why it happened.
Ayana established almost immediately after realizing Erez's romantic attraction that this was something to take advantage of. Best case scenario: he truly falls madly in love with her and becomes a powerful tool to use against the rest of the Russel family. Worst case scenario: this is all a cunning ruse on Erez's part to basically do the same in reverse against Ayana's family, but even in this case, it would be better to maintain a faux relationship to get whatever intel she can.
If your issue is more directed at the author for contriving this whole thing, this story is tagged reverse harem. Our protagonist getting into romantic situations with different men is to be expected, regardless of how small their chances seem to you. I would only expect to get more of this, not only with Erez, but Rox as well. (And maybe even an extra guy or two down the line, though I feel like this story has enough going on to not need further additions to the harem.)