I never understood how it could become Scott's territory. It was the Hales for generations and here comes this unknown beta who turns into a 'true alpha', probably so he could get the territory, but it just doesn't make sense. I love fics where the land knows that the Hales are in charge and not some young upstart that did absolutely nothing to be in the position he is. Actually he did a lot that should have been reason for him to not be in that position.
Ok, so I absolutely believe that territory means so much more than who’s the strongest Alpha around at the time (otherwise Beacon Hills would become Deucalion’s territory in 3A). Beacon Hills is Hale land, and the only reason I really acknowledge it as Scott’s territory now is because Derek willingly cedes it to him. And I tend to take that less as “you’re the Alpha, you deserve it now and I don’t,” but because Derek never honestly wanted that responsibility but he felt like he was trapped with it out of duty to his family, and now he finally trusted that the territory would be safe without him. Before the s4 finale I always saw Scott and Derek as co-protectors. Scott might have had the status and the pack (as Derek did in season 2) but Derek was in no way Scott’s subordinate. He was the sixth ranger, you know? He would do his own thing, sometimes coordinate with the main team because they had the same goals, but he still had at least equal rank to Scott. I love fics where Scott calls himself Alpha but acknowledges the land as Hale land and treats Derek as an equal in all territory dealings, because that’s how it should be. He was never Scott’s beta, and he was always there out of guardianship to the land. It was only when Derek gave Scott that nod and left town that the territory became Scott’s, because Derek allowed it to be.
And that’s honestly fine to me, because I think by that point (and maybe even by the pilot, honestly) the town had become too toxic for Derek to ever really settle, ever really be happy there, or build a real life. I always like to talk about Derek moving back to his family’s former territory – wherever the Hales lived a few hundred years ago (which I personally picture as being outside London) before they moved to Beacon Hills. I like the idea of him carrying on his family’s legacy but somewhere that’s healthy for him, fresh and void of toxic memories but still connected. Which… drifts a bit from the topic of your ask but yeah, Beacon Hills belongs to Scott only because Derek didn’t want it, because he was waiting for a chance to break away, and Scott resolving to protect the town and take charge of his own pack (which he showed attempts at doing during season 4 with Liam) finally gave him that reason.