Why did the government store the Ark of the Covenant at the end of Raiders
? Why does Stargate Command store alien technologies in Area 51 in Stargate
? Bureaucracies like to store and catalog things. Besides, secret warehouses are cool.
Seriously, I can think of several reasons for storing these technologies rather than destroying them. First, they involve powerful energies and incomprehensibly advanced technologies, so the DTI doesn't know if it can
safely destroy them. Second, studying these artifacts can help the DTI understand how temporal technologies and phenomena work and thus help them devise means of detecting them and defending against them, as well as improving their general theoretical and practical knowledge of temporal physics, which can help them do their jobs better. Third, some of these artifacts may be evidence in ongoing investigations and prosecutions and thus need to be preserved. Fourth, there's pure science -- all physics is interconnected, so these artifacts could advance Federation understanding of physics in general and open the door to improvements in fields other than time travel. Fifth, the DTI knows that there will come a time when the Federation is able to manage temporal technologies responsibly, so there might be value in preserving such devices until such a time.
And sixth, there's the Godzilla Threshold
. There may come a time when the timeline is so thoroughly screwed up that time travel is the only way to fix it. So it makes sense for the DTI to keep some time travel capability on hand just in case.