My wife and I and our adult son flew to France this summer. We decided each of us would place an AirTag in his or her checked suitcase. Like you we were unsure of whether to centralize the tracking on one phone or distribute to each person. We decided each person should track on their own phone. If any of us had not been comfortable on how to do it, we would have tracked on my phone, but everyone was fine with keeping an eye on his or her luggage. It’s kind of fun watching it in Find My as you wait at the gate and while on the plane. Is it going to make it? Part of the travel adventure.
We all agreed to share our locations the whole time we were in Europe, trading away privacy for security, so there was no additional privacy that would have been foregone by centralizing the tracking, but as I say, we decided each traveller would track their own bag.
My wife figured it was around 50/50 odds our luggage would be lost. I, on the other hand, was pretty sure that lost luggage reports are overblown–there aren’t many news reports about luggage that made it. So I doubted we would have any issues.
Our son travelled home as planned a week before we did. Our return flight was via Calgary, Alberta, and as we took off from there I saw my suitcase didn’t appear to be on the plane. My wife’s looked also to not be on the plane, but hers was in a slightly different location out on the tarmac. At first we thought it was just because there weren’t any iPhones near the baggage trains, but, uh, no, our bags didn’t make it on.
At our final destination we reported our bags lost right away but hung around for half an hour just in case. We ended up letting the others waiting for their non-existing bags that they, like ours, were likely still in Calgary.
My bag arrived at the airport a day late, and my wife’s two days late. It was great knowing where our bags were before the airline did, and they were happy we could use our AirTags to walk straight to each of our suitcases (in two separate locations in the baggage area at our airport).
Anyway, to your question, I think you and the other posters here are thinking about the right factors: ease of recovery, privacy in the family, the fun of doing one’s own tracking (if one finds that kind of thing fun), and tech ability of each of the travellers.