quantum field theory - Why gauge theories have such a success?

[This question was inspired by a identical question asked on a other forum]

Note that we may morally include general relativity in the gauge theories.

We may have several (some are deliberately contradictory) remarks :

1) Gauge invariance is only a mathematical redundancy, which is unphysical. In fact, we are not using the correct mathematical tools, and/or we have to give up the standard view of space-time (and action).

2) We can't avoid the gauge formalism, because it corresponds to something fundamental, it is not only more pratical for calculus.

3) For massless particles, it is interesting to consider the helicity formalism (the masslessness derives automatically from the formalism).