Any useful consequence of a physical effect is, in effect, an experiment that could test that effect. So if the smallest test is with a machine the size of a small country, no device using the effect can be smaller.
https://en.wikipedia.org/wiki/Effective_field_theory
demonstrably works up to the electroweak scale, which requires an LHC-sized machine to probe.
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.
The first useful internal combustion engines were room-sized, now they fit on a moped.
The truck-sized hole in your argument is talking about "the smallest test". First discoveries/demonstrations of interesting phenomenons don't typically happen at the smallest scale (why would they?).
In contrast, a particle accelerator like the LHC is designed from the outset to explore physics at a given energy scale at the lowest possible cost. Shrink it any further and it will no longer work. Despite decades of attempts to come up with alternative designs, when time comes to draw up plans for a successor capable of pushing to even higher energy, it's just more of the same:
https://home.cern/science/accelerators/future-circular-colli...
