Doublelift has been a pro for years

Exactly Freeze's point

carried teams through relegations

No... as someone following CLG for so long through thick and thin, Doublelift did not carry CLG through any of their relagations. In their first relegations match, they face Azure Cats and just completely outclassed them. In their second relegations matches vs Curse Academy, one win was a "protect the doublelift" and the other two were carried by Link and Aphro. Overall Aphro was pretty clearly the series MVP.

played with many supports

Every single one of which eventually quit on him. From Chauster, to Locodoco, to Aphro (who left CLG due to the team's toxicity), to Yellowstar. None of them speaks fondly or favorably of him.

changed his play style many times

No, that's wrong. DL has never changed his play style. This is the biggest criticism of DL. He only knows how to play "protect the doublelift" comps. He only knows how to win lane (sort of) and try to snowball from lane advantage. He is incapable of playing utility supports (Sivir, Ashe, etc.). Take this past split as an example. YS came in with an idea on how the lane should be managed that enabled YS to roam, gain vision and advantages for the team. But no, DL couldn't handle that. This is why TSM sucked all split long. By the end TSM as a team basically reverted to playing "protect the doublelift", shackling YS to the lane. This allowed them to make a deep playoff run, but it completely exposed DL's inability to change play styles.

You can look at the players through rose-tinted TSM goggles, but the reality is that DL has long-since peaked and is too entrenched in his ways to continue to grow. Mechanically, the world has basically caught up to him and his inability to play within the context of a team is holds him back.