Comment by T-A

Effective field theory is a general approach to integrate out degrees of freedom which are not relevant to the problem at hand. Trivial example: if you are trying to build an aqueduct (characteristic scale: meters and up), you can safely ignore the inner workings of individual water molecules (characteristic scale: tenths of nanometers), or even the fact that molecules exist at all.

In terms of interaction energies, once you have an effective field theory which demonstrably works well up to some scale E, you know that whatever new physics you may find by colliding things at energies larger than E will not significantly affect physics at energies lower than E.

Thanks to the LHC and its predecessors, E is now upwards of 1 TeV, or equivalently a spatial resolution of 1 attometer; a billionth of a nanometer, less than a thousandth of a proton's diameter. Anyone arguing that this still is not enough, and that a larger accelerator may reveal new physics with wonderful technological properties, must be planning to go live inside a proton.