What would be the advantage of that over doing zillions of particle interactions in an actual particle accelerator?
If history is any guide then theories of physics are extremely simple. All the way from classical mechanics to special relativity, general relativity, quantum mechanics, quantum field theory, the theories are simple. In fact in some sense our theories have been getting simpler.
Take for instance the step from classical mechanics to special relativity. In classical mechanics time and space are not on equal footing. Time is the independent variable, and the space coordinates of particles are functions of time. In special relativity these are put on equal footing, and this simplifies the physics. It's not easier, but it's simpler in the sense that there are fewer parts. You used to have energy, and x-momentum, y-momentum, z-momentum for the 3 spatial directions. It turned out that energy is t-momentum in the time direction. This simplifies the equations because instead of having one equation for energy and another for x,y,z-momentum, you have one equation for x,y,z,t-momentum. Symmetries between electric and magnetic fields in Maxwell's equations were discovered that unified them into one object, just like with energy and momentum. A similar story exists for quantum mechanics.
What you suggest about modeling physics as a black box has been suggested before. After the first particle accelerators were built people were finding lots and lots of new particles, and there wasn't any good theory for them. Some people thought that we had to give up on a theory, and just model the real world as a black box of X particles in -> Y particles out, and make a big database of such interactions. However, then the standard model came along and all those particles turned out to consist of a much smaller number of quarks that interact in a small number of definite ways.
With string theory however we are in precisely the opposite situation. We don't have a big amount of experimental data that we need to find a theory for. We have a large number of theories and no experimental data to distinguish them.
If history is any guide then theories of physics are extremely simple. All the way from classical mechanics to special relativity, general relativity, quantum mechanics, quantum field theory, the theories are simple. In fact in some sense our theories have been getting simpler.
Take for instance the step from classical mechanics to special relativity. In classical mechanics time and space are not on equal footing. Time is the independent variable, and the space coordinates of particles are functions of time. In special relativity these are put on equal footing, and this simplifies the physics. It's not easier, but it's simpler in the sense that there are fewer parts. You used to have energy, and x-momentum, y-momentum, z-momentum for the 3 spatial directions. It turned out that energy is t-momentum in the time direction. This simplifies the equations because instead of having one equation for energy and another for x,y,z-momentum, you have one equation for x,y,z,t-momentum. Symmetries between electric and magnetic fields in Maxwell's equations were discovered that unified them into one object, just like with energy and momentum. A similar story exists for quantum mechanics.
What you suggest about modeling physics as a black box has been suggested before. After the first particle accelerators were built people were finding lots and lots of new particles, and there wasn't any good theory for them. Some people thought that we had to give up on a theory, and just model the real world as a black box of X particles in -> Y particles out, and make a big database of such interactions. However, then the standard model came along and all those particles turned out to consist of a much smaller number of quarks that interact in a small number of definite ways.
With string theory however we are in precisely the opposite situation. We don't have a big amount of experimental data that we need to find a theory for. We have a large number of theories and no experimental data to distinguish them.