Hypersonic reach does not automatically replace carrier aviation

Would a fighter able to cross the world at hypersonic speed make fixed-wing carrier aviation obsolete?

Not automatically. Routing, maneuver, persistence, rearming, and continuous local air cover may still make a carrier valuable even when transit speed becomes extreme.

A very fast land-based fighter can reach distant seas more quickly, but it still needs a safe route and may require overflight permission. Hypersonic flight may also constrain turning, basing, payload, and fuel in ways hidden by a simple speed figure. Most importantly, an aircraft that dashes out, fires, and returns cannot remain over the fleet while the next threat arrives. A nearby carrier continues to provide persistent patrol, rapid rearming, and a mobile base unless the new technology solves those operational problems as well.