If we had absolutely all the evidence, a perfectly preserved body in formaldehyde for every organism that ever lived--never mind where this repository is supposed to be stored--we would according to evolution have a record of smooth transitions which outlines a tree of common descent. The traditional problem from Darwin's day forth is that geology doesn't give us such a perfect record and, as Darwin himself noted, it never will.The biomass you take out of circulation (essentially all of it that ever lived) in preserving such a record would change the history of life on Earth forever and at once. Just for one thing, nothing is allowed to eat anything else. Carnivores and scavengers could never have evolved. Animals of any sort could only get so far, would probably have died out early in the history of life. Plants would have to do without something of which they make great use now: nutrients from decomposed organisms.
In trying to keep such a record, you would have a Heisenbergian measurement-changes-what-it-measures problem in its most extreme form. Better to just sample lightly, take some DNA, and snap some pictures.