Greg...
The Poco -- for Service Drops -- figures on their experience -- and on the fact that such conductors are in Free Air.
3/0 XHHW-2 (90c) Aluminum is rated 275A in Free Air -- continuous duty. And that has to be a conservative rating, to boot.
The cyclic nature of hot tubs means that they don't run loaded up for 180 minutes of continuous draw. Further, the hotter the weather, the less they draw. Cold weather for the load also means more cooling for the Service Drop.
BTW, I never hear of any hot tub using heat pumps. For southern climates, such devices would do the trick for not a whole lot of cash.
For you never see patrons of the hot tub running out in the ice and snow to use them; and that's the only time they wouldn't pencil out.
