This also helps avoiding constant interruptions or context switching to the whole team that are now handled by the designated person of the week.
As an added bonus, this incentivizes better documentation of your system via runbooks (I'd rather point someone at a doc than walk them through a problem when it's not my week).
And eventually employees burn out and start mailing in that week and now suddenly nobody cares except the other teams having trouble getting support, but apparently that is a diffuse enough complaint that nothing ever came of it.
Not that I speak from experience...
That works out to leaving one team member a full sprint for a deeper heads-down task.
To alleviate some of the extra load on the on-call rotation, we dedicated a decent portion of our sprints to automation for a few quarters, which allowed us to reduce some of the recurring manual tasks and ease the load on the on-call role. Now the on-call person will usually see an average 15hrs of support on the regular (of a 40hr week), down from damn near 35hrs.
That is to say there was about 20hrs of automatable tasks that had been shouldered by one team member for years. When that person left the tasks were placed onto the on-call rotation as a duties as a way to ensure every team member became familiar with these tasks instead of being siloed into a single person (there was a scramble to learn those tasks as this person was offboarded, and a rough couple of months as we skilled up on these).