It's not simply giving up being a Royal for love, it's giving up who he is - and his family - for it. Being a Royal is what he was born to do and what he was raised to do. He might not like every aspect of it, but both he and William have shown that it's something they consider to be a part of their lives. The Royal Duties is as much their job as their military service, and both seem to accept that eventually being full time Royals is their future. Every expectation seems to be that with time the senior Royals will do less while William, Catherine, and Harry do more, and none of them have given us any reason to believe that this is contrary to their own desires.
If it was, then Harry could theoretically give it up for love (or whatever reason) and hope that in doing so the press will stop following him (which seems highly unlikely). Except to give up the Royal Life is to go back on his destiny so to speak and to renege on his duty. Sure, Harry might come across as immature and reckless at times, but I can't see his family calmly accept him giving it up. In my mind, with an understanding of how the BRF reacted to the abdication, to give up being Royal would entail giving up being a member of the family. I can't see HM or The DoE calmly accepting Harry's resignation and allowing him to stick around in the background at Balmoral, not can I see The PoW doing so either. Harry might retain relationships with them, but they'd be strained at best. Similarly his relationship would become strained with William.
Furthermore, what kind of woman would really ask someone to give up his job, his life, and likely his family? That doesn't sound like his one true love to me, that sounds like someone who's demanding and a bit selfish. While I think Harry and Chelsy may have been great together, if she had in fact asked him to give it up before they got married I would have thought less of her for asking and him for doing so. And that's assuming that Chelsy was in reality the love of his life. We don't know that, and when it comes down to it really we have no reason to believe so. Chelsy was a girl he dated, yes for a long time, but note the past tense. She is now his friend, nothing more. Both appear to have moved on, both may still find the love of their life. For all we know, the love of Harry's life could be Cressida Bonas, we don't know yet.