Exactly what I have been brainstorming a couple of times recently. I think it's a really cool idea, although I wouldn't know why anybody would want to switch? It would probably become rather niche (which is possibly even for the best). And if a critical mass switches over, what would prevent it from having the same kind of people and behaviour?
That being said I would be absolutely down to go down that rabbithole.
Why would a Twitter user switch to Mastodon or Bluesky or micro blogging, either on a shared public instance or on a personal instance?
Why would anyone think of making a new Twitter or a new LinkedIn in 2015? (actually, it's not new, it's different because of the different premise: not a single private platform controlled by whoever owns it, but several cooperating platforms through a common protocol).
Why would a Ford driver switch to a bicycle? Because while the infrastructure has not adjusted yet, it's a more sustainable, human-sized, city/neighbourhood-sized transportation tool (which, while it does not cover 100% of the cases, depending on the situation, can cover 50/80% of those), and it gives, not more power (that's irrelevant) but much more direct control about what you can do with it, where you can go.
So in short: it cannot start differently than as a niche thing.
> if a critical mass switches over, what would prevent it from having the same kind of people and behaviour?
Hosting instances policies and moderation. Much like Mastodon does already.
The actual value/service of LinkedIn is not in the data they have (it could be as well stored in a distributed database, such as the open web could be understood as). It's in how they operate/categorize/filter/report over it (their algorithms), and how they brand under their authority (which some take as some guarantee, which they are even happy to pay to).
That being said I would be absolutely down to go down that rabbithole.