I wouldn't call it a strict 'best practice' as it depends on the policies / individual situation of the end user.
That said, wanting "operators to focus on the present" is not a common reason I know for disabling access to recorded video. Operators are not generally super interested or distracted by recorded video.
On the other hand very large organizations do typically divide live monitoring and investigations into separate teams / individuals. To that end, restricting the live monitoring team from searching for video makes some sense.
As for your example of not allowing to see all but the "most recent 5 minutes recorded history", I am not sure what VMSes support that. Most systems have user permissions for recorded video but it is all or nothing proposition (at most at a per camera level). I don't know what VMSes let you set a max time frame that a user is allowed to search video. Anyone with info on that, please share?
It is the customers call obviously, but my personal preference is operator has hands off recorded video. I have seen operators do "fishy" things with recordings only to find out later there was an inside job going on. When asked, that is advice and my reason.
The original Bosch BVMS allowed that feature. I don't know about recent versions.
Ocularis allows you to restrict access to playback on a per-camera basis - either by denying access completely, or limiting how far back an operator can view specific cameras (in hours though, not minutes).