All of the following is my understanding of the current situation and
concerns based on what I've read in the news and other public information.
There appear to be two separate types of documents here that are of concern
to the government:
- Records produced by the Trump administration. These may or may not
contain sensitive information, but that doesn't matter: but the key
point is that the government does not have those records; they were
removed from government offices when Trump left office.
- Documents produced by other parts of the government that contain
sensitive information and thus are classified under the United
states government classification system (as Confidential, Secret,
Top Secret etc.).
Your question does not appear to be concerned with the latter, so I won't
address those further except to point out that it should be obvious why the
government would be concerned whether classified documents are stored
securely and why they would attempt to retrieve any copies that they feel
are not stored with sufficient security.
(A third type would be non-confidential documents produced by other parts
of the government; these are of no concern because the government still has
their copies and thus has no need of the Trump administration's copies, nor
any need to protect the Trump administration's copies.)
The records produced by the Trump administration are, by law, owned
by the public and the government is legally mandated to preserve copies of
them. The government apparently does not have copies of some of these
records produced by the Trump administration, so they're trying to get
copies, as is their legal obligation. That's all.
The idea that the Trump team could have made copies (digital or paper, and
uploaded to the cloud or stored elsewhere) isn't relevant at all to this;
there's nothing saying that Trump can't keep copies of whatever they like
that they've generated. (This might even be done at the time the records
are generated; the law mentioned above allows you to create/send electronic
records through non-official accounts so long you, at the same time or
shortly thereafter, send a copy to an official account that's properly
archived.
It's certainly possible that the Trump team could have destroyed (shredded,
burned, whatever) the records that the government is trying to retrieve
copies of. But that's not particularly relevant, either; it's never
guaranteed that when you execute a search warrant you'll find what you're
looking for. If one should never do a search when you can imagine some
circumstance where the search would fail, you'd never search for anything.
Imagine a parallel situation: you let a friend use your workshop to help
you build a birdhouse, and later you discover that the dowel for the perch
you were working on together is missing, and hear that your friend took it
to his workshop. You can imagine the possibility that he took it to his
workshop and burned it; does that mean you don't go there and look to see
if it's there or not?
You also use, several times, the term "evidence." Whether these documents
are evidence of anything or not is no concern of those attempting to fulfil
the obligations of the Presendential Records Act; the government must
preserve copies of these documents regardless. If other parts of the
government later wish to claim that any of those documents are evidence of
something or other, they may have access to them in order to support their
claim, but that's nothing to do with the PRA itself or the obligation of
the government to preserve these documents. They must be preserved even if
nobody claims that they're evidence of anything at all.