That's not how trust works in Ripple. The trust line only exists for the instant the payment is made. Otherwise, each extension of trust is independent of every other one.
If you trust B, presumably it's because you entered into an agreement with B such that they have an obligation to settle their debts with you. What interaction they have or don't have with C is none of your business. Either B makes good or they don't. If they don't, then they are betraying your trust. Nothing C, D, E, or F does has anything to do with it.
That's great in theory, but it's not going to work in practice because
nobody is 100% trustable. The blockchain, on the other hand, becomes nearly 100% trustable with a high amount of transactions, and/or checkpointing in the client.
It's like if I send you a check for $50, you deposit it in your bank, and then your bank goes out of business without paying you. It's not my problem. I only chose to trust *my* bank. Once you take the $50 as payment, how you settle with those you chose to trust is your issue. (When you set trust, you are essentially setting what you are willing to accept as payment.)
Again, this sounds great if you just have a few hops. But once you get to a large amount, people will start realizing they're losing all their money because of covering for scammers, people who died, etc.
It's not going to work in practice, and is just a disaster waiting to happen once a sufficiently trusted person / gateway collapses.