I have recently encountered Haag's theorem and according to Wikipedia:
Rudolf Haag postulated  that the interaction picture does not exist in an interacting, relativistic quantum field theory (QFT), something now commonly known as Haag's Theorem. Haag's original proof was subsequently generalized by a number of authors, notably Hall and Wightman, who reached the conclusion that a single, universal Hilbert space representation does not suffice for describing both free and interacting fields. In 1975, Reed and Simon proved  that a Haag-like theorem also applies to free neutral scalar fields of different masses, which implies that the interaction picture cannot exist even under the absence of interactions.
Studying some particle physics, this kinda bothers me. Also the article says:
While some physicists and philosophers of physics have repeatedly emphasized how seriously Haag's theorem is shaking the foundations of QFT, the majority of QFT practitioners simply dismiss the issue.
And not to worry about this is exactly what my particle professor recommended. I understand that evidently physicists are doing pretty well in calculating their scattering amplitudes with the interaction picture, but this as an explanation is just saying that the end justifies the means. It doesn't really comfort me when there is still a mathematical proof saying that the interaction picture just cannot exist. Now, is it okay to worry? (Why not? - Besides the notion that it just works, which sounds a bit like magic to me)