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HoG pays for itself in 27 mins, or half that time if you decide to sell it. In the meantime, you do get 250 health, which every point counts since you won't be building more hp outside Shurelya/Tri-force. And 250hp by lvl 11 is like 17% increase in hp (more at earlier levels, like 25% increase at lvl 6), which is significant when your biggest threat in mid-game are the bursts from AP carries.
Finally, there's enough gold in the jungle to have both philo + boots 1 after your first clear, and HoG before the 10 mins mark (usually around the 8 mins mark after you give blue to mid). Nothing is really stopping you from building HoG, get Frozen Heart, then sell HoG once you need your 6th slot.
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