Where does the 43% number come from? That is an oddly specific number for the large energy range of cosmic rays - most of them way above 43% the speed of light.
Accelerating a proton to 43% the speed of light needs an energy of about 0.1 GeV. The LHC accelerates protons to 6500 GeV. Even if cosmic rays would produce a nicely collimated beam (they do not) it wouldn't be worth catching it.
The highest rate of cosmic rays at the ground comes from cosmic rays muons, of the order of 1 per cm2 and minute. 1 cm2 is larger than a typical beam but let's use that to be optimistic. About 1 in 1000 of them are in a (very generous) suitable direction (<1 degree off). That means we get maybe one muon every 15 minutes, and that is very optimistic. Muons also decay within microseconds so we can't store and accumulate them.
The LHC accelerates bunches of 1011 protons, separated by 25 ns, corresponding to a current of 4*1018 protons per second, 21 orders of magnitude more than our cosmic ray capture process.
The collision rate in a collider scales with the product of the beam currents (+some other factors I neglect here). Our cosmic ray capture muon collider would have 42 orders of magnitude disadvantage. That is a factor 1000000000000000000000000000000000000000000. We would never get even a single collision out of it.Does that mean cosmic rays are useless? No. They are always available, and sometimes they save you the effort to build an accelerator. Particle detectors need to be tested before installation, and the relative position of all their parts needs to be known as accurately as possible, ideally before starting the main physics measurements. In both cases cosmic muons are a nice tool. They are a free source of reasonably high energy particles going through the detectors.