###No.

There is nothing wrong with perturbation theory, or with theories with known, restricted accuracy. The point of theory is to explain the results of observation from as simple an initial theoretical standpoint as possible. Therefore:

1. Since experiment always has a finite uncertainty, one can only ask that theory match the experimental value within its uncertainty range. Exact answers are not very useful in physics, because we know that other, smaller effects will always get in the way before an experiment matches the infinite set of significant figures we can draw out of an 'exact' answer. Ignoring these effects, or trying to minimize them, is very often the best way to hide your head in the sand while some amazing physics walks by.

2. The point of theory is to make the initial standpoint as simple and understandable as possible, and to try and get some intuition for how that standpoint implies experimental results. It is a fact that most simple models will in general not be solvable. More importantly, it is not a given that the universe is describable by solvable models. We're not out to impose structure on nature, we're out to find the structure that's there. If it turns out it's not an exactly solvable model, then that's the way it is.

No.

There is nothing wrong with perturbation theory, or with theories with known, restricted accuracy. The point of theory is to explain the results of observation from as simple an initial theoretical standpoint as possible. Therefore:

1. Since experiment always has a finite uncertainty, one can only ask that theory match the experimental value within its uncertainty range. Exact answers are not very useful in physics, because we know that other, smaller effects will always get in the way before an experiment matches the infinite set of significant figures we can draw out of an 'exact' answer. Ignoring these effects, or trying to minimize them, is very often the best way to hide your head in the sand while some amazing physics walks by.

2. The point of theory is to make the initial standpoint as simple and understandable as possible, and to try and get some intuition for how that standpoint implies experimental results. It is a fact that most simple models will in general not be solvable. More importantly, it is not a given that the universe is describable by solvable models. We're not out to impose structure on nature, we're out to find the structure that's there. If it turns out it's not an exactly solvable model, then that's the way it is.