Cosmic rays energies can exceed $10^{8}$ TeV, way higher than the energy scale achieved in the LHC or that can be achieved in the near future.
cannot we just use them to study fundamental interactions at such extreme energy scales, instead of LHC?
What are the difficulties in guiding and channeling such super high energetic particles and make them collide to probe fundamental physics at such super energy regime?
The short answer is "we do" (see Pierre Auger Observatory and others1), but it's not like you can build a CMS equivalent at the one spot in the whole atmosphere where a $10^{19}\text{ eV}$ cosmic ray is going to hit next year, so we do a different kind of particle physics there.
A typical ultra-high energy cosmic ray observatory combines an array of ionizing particle counter ground stations with one or more air fluorescence telescopes to attempt to sample and reconstruct both the total energy of the events and the geometric parameters of the shower. There data are then compared to the results of simulations to pick out the most likely values of certain parameters of the model that are not well constrained by other data.
On the astrophysics side the data constrain the rate and ranges or the kinds of energetic events that can impart these ridiculous energies to particles.
1 Possibly to include Auger North on the Kansas-Colorado border in the next decade.
One major problem with this proposal is that the cosmic ray hits a particle at rest, not another cosmic ray with the same energy going in the opposite direction. Under these conditions, if a cosmic ray proton at enormous energy E hits a proton at rest with mass m, the center of mass collision energy is found by boosting to the rest frame, and the result is a collision at energy
$$ E_\mathrm{cm} = \sqrt{Em} $$
This center of mass energy is not so high. The geometric mean of 10^9 TeV and 10^{-3} TeV is 10^3 TeV, within range of conceivable Earthbound accelerators, where you can have a high luminosity and know what you are banging. If you hit a heavy nucleus, the center of mass can be pushed up by a factor of 10, at the cost of a more complex event.
Even if you use the rarest and most energetic cosmic rays, you only get another factor of 1000 in center of mass, so you don't cross the desert and make a black hole. That would only happen for a head-on collision of the most energetic cosmic rays somewhere in deep space.
Energetic cosmic rays are rare, as @John Rennie states in his answer, and the detectors to measure their effect cover kilometers. One high energy entrant creates what is called an air shower and it is measured as @dmckee describes.
It is not possible to use them as an incoming beam because we do not know what they are ( except in the case of gamma rays and neutrinos, because they need special detectors), so we do not know the incoming beam, and do not know where the interaction happened. They are interesting events but new physics can not be garnered from the observations.
The observations are useful for astrophysics though and cosmological theories.
We actually use cosmic rays to study fundamental physics. Thanks to them we discovered the muon and the positron many years ago, as you probably know, and currently they imposes severe constraints on violations of Lorentz invariance.
The tension between cosmic ray physics and accelerator physics is the tension between observations and experiments. In the former one is not able to fine the experiment: one cannot choose the particles or their energies and directions. However, the energies are much larger than in terrestrial accelerators.
Likewise, hadronic accelerator like LHC or Tevatron attain larger energies than leptonic collider like LEP since energy loss by synchroton radiation increases with a negative power of the particle mass. However, hadronic accelerators are much dirtier than leptonic collider since hadrons are not elementary particles. As you see there is a tension. Hadron colliders (and cosmic ray physics) are well-adapted for big discoveries, but they are not for precision test. The next large accelerator will probably be a linear leptonic collider in order to improve the precision (for this it will be leptonic) and not to lose synchroton energy (for this linear).
The density is far too low, you can't predict where they will arrive and when, and you don't know the incoming energy. Apart from that they would be perfect :-)
Seeing something decay into a Higgs or something new and unobserved is extremely low-probability. If I remember right, it's something along the lines of millions of proton-proton collisions in order to observe something like 10 Higgs particles created. There's no way to get anything approaching this luminosity with cosmic rays, which will overwhelmingly hit the atmosphere and engage 'boring' QFT processes like Compton scattering, muon production and blah blah.
