Haag theorem says the so called interaction picture as seen in QFT doesnt exist. The S matrix is assumed to be unitary "like a rotation" and found not to be unitary. Interaction hamiltonian said to be a non existent mathematical entity.
Physicists casually state these things and then say "but it works muh beauty".
How do you consciously do shitty mathematics and find out (sometimes) good results?
Having computers algebra on hand, isnt it much easier to just solve these non-lineal interaction lagrangians with brute force and infinite series and deal with it?