It's an interesting idea but, if I understand it correctly, I don't think it would be able to capture the majority of particles emitted from the collision zone. Modern detectors are designed to be as hermetic as possible so they can capture as much of the transverse energy as possible. This is crucial because in the plane perpendicular to the beam axis (i.e. line of collision) the total momentum is zero. Thus we can use conservation of momentum to infer the presence of particles that the detectors struggle to find (like neutrinos). This, of course, only works if we're confident that we accounted for (almost) all of the particles coming out of the collision.
Here is a picture of a heavy-ion collision reconstructed from the CMS detectors to give you an idea of how much needs to be accounted for [0]. The light orange lines are the particle tracks in the tracker, the red boxes indicate the amount of energy deposited in the EM calorimeter, and the blue boxes indicate the amount of energy deposited in the hadronic calorimeter.
I should note that normal proton-proton collisions do not produce anywhere near this number of particles (what we call the event "multiplicty") but they can still produce a few hundred. Furthermore, there are, on average, 40 proton-proton collisions per bunch crossing (which is what dictates the 40 MHz rate). So every 25ns there is a bunch crossing and the detector "snaps an image". In that image there are typically about 40 different collisions. Correlating tracks to vertices is not that easy given these conditions and is further complicated by the fact that particles can decay mid flight, causing their track to suddenly change. It would be great if we could be absolutely confident about the physical quantities associated with all of the particles produced in a collision, that's all we would need to know and this is essentially what's produced in high-energy physics simulations. However, reality is a lot messier. In addition to what I previously mentioned, the interactions between the detector material and the particles themselves also creates a lot of noise in the system. All of these uncertainties make it infeasible to compress an event down to just the reconstructed physical quantities, there is too much uncertainty and I don't think it will ever be overcome.
Lastly, I should mention that the energy densities reached in the immediate vicsinity of the collision zones is high enough to destroy any material known to man. The center of heavy-ion collisions reach a temperature of over a trillion degrees. That's 100,000 times hotter than the center of the Sun. No instrument could ever be placed there to make an accurate reading. The best we can do is place detectors a decent distance away (IIRC it's about a few cm) and try to catch what comes out.
Here is a picture of a heavy-ion collision reconstructed from the CMS detectors to give you an idea of how much needs to be accounted for [0]. The light orange lines are the particle tracks in the tracker, the red boxes indicate the amount of energy deposited in the EM calorimeter, and the blue boxes indicate the amount of energy deposited in the hadronic calorimeter.
I should note that normal proton-proton collisions do not produce anywhere near this number of particles (what we call the event "multiplicty") but they can still produce a few hundred. Furthermore, there are, on average, 40 proton-proton collisions per bunch crossing (which is what dictates the 40 MHz rate). So every 25ns there is a bunch crossing and the detector "snaps an image". In that image there are typically about 40 different collisions. Correlating tracks to vertices is not that easy given these conditions and is further complicated by the fact that particles can decay mid flight, causing their track to suddenly change. It would be great if we could be absolutely confident about the physical quantities associated with all of the particles produced in a collision, that's all we would need to know and this is essentially what's produced in high-energy physics simulations. However, reality is a lot messier. In addition to what I previously mentioned, the interactions between the detector material and the particles themselves also creates a lot of noise in the system. All of these uncertainties make it infeasible to compress an event down to just the reconstructed physical quantities, there is too much uncertainty and I don't think it will ever be overcome.
Lastly, I should mention that the energy densities reached in the immediate vicsinity of the collision zones is high enough to destroy any material known to man. The center of heavy-ion collisions reach a temperature of over a trillion degrees. That's 100,000 times hotter than the center of the Sun. No instrument could ever be placed there to make an accurate reading. The best we can do is place detectors a decent distance away (IIRC it's about a few cm) and try to catch what comes out.
[0] http://cms.web.cern.ch/sites/cms.web.cern.ch/files/styles/la...