Double check everything, since Siemens makes several lines of breaker/panel (which are physically incompatible so they plainly won't fit), but it all makes sense to me.
- You made a canny choice of hot tub subpanel so you could swap breakers - smart economics.
- The farther upstream the GFCI protection is, the better - and you can't get more upstream than the main panel, can you? :)
- The breaker in the panel is able to protect the #6 cable and 60A subpanel.
- The breaker has the correct thresholds for a hot tub (8ma and not 30ma) since it's sold as a hot tub panel.
- With the subpanel fully GFCI protected, you can put plain breakers in there. Though a typical dumb home inspector isn't going to like it.
Be sure to put "GFCI Protected" labels on the receptacles and subpanel, I recommend making your own with a common labelmaker, as they last longer than the blue paper ones that come with GFCIs.