Oh wow! In my country, legal documents like this arrive with a QR code or confirmation code attached that can be used to verify legitimacy of the document on the official e-government internet site.
I worked in a data center once, and we would have FBI contacts that would come in regularly to access criminal data (CP, terrorist communique, heavy piracy, etc). We would verify the warrant before secure entry+accompany them to the specific requested entity. I know procedures are similar + even more stringent for the medical field. Things get even more complex for small local authorities, but the idea that "just having a slip of paper" is enough is ridiculous; unless the person accepting the request is dumb/lazy/uninformed/undertrained/etc, as in any social engineering feat (in your case, the responsible person decides to not bother with the QR because their phone connection is bad, it takes too long, etc; for example).
So it's not like on TV where if they have the paper they can just show it to you and barge past you by force?
For arrest warrants that makes sense, but they portray search warrants the same way.
Even in these cases, they still have to give you the warrant and you're able to take it up with the issuing authority/take to court the executing officers.
But yes, arrest warrants and personal search warrants can be executed expediously for evidentiary / flight concerns. It's the exception, not the rule.