He's done loads of stage musicals, it's not like he's unused to live performance. But I guess that Strictly is a one-off pressure of a different sort, more what the sportspeople are used to. Musicals are designed/choreographed to be achievable by the performers reliably eight shows a week, so although things can go wrong, they're normally bit of pitched in your range of ability with a little margin for error. If you cock it up you've left a thousand paying punters fuming.
On Strictly Katya in particular choreographs right to the edge of her celeb's ability and a tiny bit beyond, and that's fine, because the potential for cockup is part of the show - it's built on a triumph or disaster narrative. Solid competence and dancing safely within your limits will get people switching off.