> An administrative subpoena implies that there has been a legal procedure and the administrative agencies are not exactly run like the wild west

Hard disagree. The fact that a government agency "reviewed" its own subpoena before enforcing it does not follow the spirit of the Fourth Amendment, which is to prevent government overreach in taking your belongings and information.

In fact, to take your definition of what's not unreasonable to its logical conclusion, by definition any process an agency came up with would be acceptable, as long as they followed it.

I think a better definition of a reasonable search and seizure would be one where a subpoena goes before a judge, the target of the subpoena is notified and has the opportunity to fight it, and where there are significant consequences for government agents who lie or otherwise abuse the process of getting a subpoena.