It's exactly how I did it when I was responsible for Board meeting minutes. I held dual role of Finance Director and Company Secretary. The Board meetings were confidential and we didn't have a proper secretary we could trust implicitly. So I got the job, as I was ultimately responsible as part of the legal duties of Company Secretary.
A lot of the discussions were way over my head, particularly on complex technical matters (design, manufacture and installation of cutting edge electronic connectors). If I'd just provided my random jottings of who said what about what, it wouldn't have been any use to anyone. So, I took my notes during the meeting, but asked all participants to give me their summaries of the meeting too. I then drafted minutes based on my notes, supplemented by their notes, which I circulated and invited everyone to make whatever amendments they thought were needed. Once everyone was happy, they were formally distributed.
I've seen far too many minutes which aren't even as useful as a chocolate fireguard, full of ambiguity, absence of any proper detail, etc.
Also, unless you've a recorder or can do shorthand, you probably can't write fast enough to make a proper record. If you're an actual participant, you end up concentrating too much on note making and not actually making your own contribution from your own areas of expertise.
In the absence of a proper/dedicated secretary, then I think making it a collaborative matter is the only way to do it properly.