I don't see any major problems with fungibility as what level of chain you use depends on how much fees you are willing to pay, and this also is directly dependedent on how big in value the transaction is. So if I want to sell you a bitcoin, you just tell me what chain "path" you are on, and I send it to whatever level on that path you want. The higher level, the more fees, just like with a bank or with postal mail, you pay more fees for more security for the transfer.
Sure, but is that complication, reduction in security, and damage to fungibility, worth the increased throughput? I'm not so sure it is.
"Checkpoints" could be added after a certain block depth, which would sort of "tie up" all the lose chains, but that seems like just increasing block sizes, except messier.
And also, it is annoying that Peter R used the same term "subchains" as me.
Not the first or last annoying thing he's ever done...