The movie would have been just fine without that entire side story. It felt awkward. It didn't fit.
shareSophie needed something to overcome just as Alex did. Agreed that it was definitely a weaker part of the film, but it did serve a purpose.
shareAlso, it gave depth to Drew Barrymore's character, made us understand why she acted the way she did. Plus, it served to show why she was 'weak' and how Hugh Grant cared for her so much by trying to make her overcome her fear of her ex and stood up for her.
shareYes, it really gave him a chance to be a hero. She was about to lose her opportunity to tell her hurt feelings and Sloane would never hear them. Hugh Grant insisting on bringing that message showed how much he appreciated the injustice of the situation.
(Of course, later, he takes two steps back after taking that step forward...)