This is a really good way to look at it! Offer up a bit of a ‘reward’ for her making the prudent choice. Also, as someone who did study abroad I can say without question that it was the best part of my college experience. Six-figure debt could indeed be crippling.
There’s also a decent chance that she would look at grad school- so having her complete her undergrad with minimal/no debt while getting a degree from a top-flight university with money to spare is a blessing. Her future self will thank you for steering her in the right direction.