(Now former) people manager here. I had what I think was a pretty good system for managing a completely remote team that did very little group-based on work together:
1) Biweekly staff call. This was scheduled for an hour, with the understanding we would end it early if we ran out of things to talk about. Normal topics were company updates, new initiatives our team was expected to participate in and an open forum for discussion amongst the entire team.
2) Bi-weekly 1:1 calls, offset from the bi-weekly staff call. I set these for 30 minutes, but had a buffer in case they went long. These were the standard 1:1. For new hires, these were weekly for the first 6 months or so.
3) Adhoc communication in-between via text, Slack, Zoom, etc.
You (OP) mention not feeling like you need the calls. You are not alone in this feeling, and it might not be a “feeling.” You might not need the calls. When I was an IC, I never really understood the need for the calls either - if I needed something from my boss, I’d call him up and ask. Some people are like that.
When I became a manager, I scheduled those calls because that’s what you’re supposed to do and I was very concerned about doing what I was supposed to do. I hadn’t ever been a manager before, didn’t really know what I was doing, and had just been handed the reins of a high-producing team.
That said, I found most of the team did want an individual touch point. Some just wanted to shoot the breeze for a bit, others wanted to talk through a problem they had or show off something cool they had been working on. One guy scheduled his own 1:1 before I could and every time had a checklist he would go through, describing every significant thing he had worked on since we last spoke.
Over time, I evolved to the system I described above. My main goal was to ensure I talked to everyone at least once a week, mainly to make sure they were ok and didn’t have any un-aired needs. At our company we had lots of meetings and lots of conference calls, so I figured the bi-weekly cadence would cut down on the meeting load for my team at least a little.