I can't agree with that. As someone who thinks Dark Phoenix Saga is the best thing ever, Claremont had a lot (a LOT) of incredible stories after John Byrne left. Brood Saga, Lifedeath I and II, Wounded Wolf, Wolverine miniseries, God Loves Man Kills, Asgardian Wars, Mutant Massacre, Inferno... Storm and Kitty Pride's character developments was all after him, for example. Not to mention the whole of New Mutants, which is consistently amazing from the Demon Bear Saga until he leaves.
Byrne, in fact, fucked up a lot of X-Men related storylines afterwards: Jean in a cocoon and Phoenix being a copy of her, Magneto being a villain again, etc.
I'm not saying post-2000s Claremont isn't pretty shit, because he is. What the hell was that New Mutants Forever...
This is totally true. Probably the best thing about Claremont was how good of a team player he was. The sinergy between New Mutants, X-Factor and Uncanny X-Men when he and Simonson were writing them. How he spun editorial mandates like Jean not dying, Jean coming back, Colossus breaking up with Kitty, etc into solid gold storylines. How he incorpored a frankly bizarre miniseries by Ann Nocenti into X-Men canon seamlessly (Longshot, Spiral, Mojo, the Mojoverse...). The Wolverine miniseries with Frank Miller. The willingness to go big into weird territory when Bill Sienkiewicz was on New Mutants. The list goes on and on.