Let's tale it at face value that a hard drive on the moon does not entropy. Let's also take it as given that the data is so important that you would pay millions of dollars to place it on the moon and millions more to get it back when needed in the event that all your other forms of backup failed due to some global catastrophe.
1) At the moment, we can't even get living people off the international space station let alone land on the moon and take off from the same spot twice.
2) If a space based proof of concept was practical, why would we not store our hard drive on the ISS. It is looking for some excuse to remain in operation and we can already come and go from it on a semi-regular basis?
3) If there was a global catastrophe to the extent that only moon based archives remained, then how are we going to go get them? This crisis destroys all data archives but preserves our space program?
4) Once we did get the drive back, what exactly might we do with it considering all other forms of data storage were destroyed?
5) If the data on the drive was so valuable that we were willing to pay millions of dollars for the chance that after Armageddon we could still get it back... Then why would the Chinese not just wait for us to place the drive then go get it themselves? Surely you would never encrypt it as the key would be just as vulnerable to loss as the data.