>that node becomes your gateway to the world wide web of Lightning nodes
My point is that you need to constantly have your lightning node running to service the channel. Whereas before with SPV or something you don't need a constant connection to the bitcoin network, and you can just receive transactions offline. That basic use case is necessarily gone in lightning.
>just to steal a few dollars
It's never just "a few dollars" because the amount in the channel needs to be much greater than the fees to open and close it. It is always a serious amount of money. This is the type of issue that gradually gets worse as bitcoin becomes more widely used, which it won't (because of issues like this).
The thing about payment channels is that bitcoiners use them to make up for the low transaction throughput caused by bitcoin's outdated 1MB block size, but payment channels are most efficient when the fees to open and close the channel are low, and there is little risk associated with closing a channel.
Want to break the lightning network? Just open a massive number of channels, then maliciously close them all at the same time. Because bitcoin's transaction throughput is so low, you can create enough channels such that not everyone will be able to close the channel at low enough fees.