So I guess the question is where is the user at on the tree. Figure 4 on plasma whitepaper (page 6) shows the user on a 3rd tree depth chain. Could she directly transact with a user on a different 3rd tree depth chain? I doubt it because that user does not necessarily know every user on other child chains.

Right. The point I'm trying to make is why are you assuming this use case matters? Additionally, all independent blockchains inherently have this issue. With your logic, the only solution is to have one blockchain, so we support this random use case you've thought up.

A second, and more likely way, is the user could send the transaction up to the parent, who knows all users on their child chains, and the parent could facilitate a transaction back down the chain. This would take longer than a direct transaction between two users on the same child chain. That is what leads me to my point of less connections.

Yeah, sorry, let me fix my comment, it was supposed to say:

But that would be goofy because all child transactions are written to the parent blockchain, which creates a domain with all child transactions.

So I was trying to say what you just said, but I left out of a word.