you need to constantly have your
lightning node running to service the channel
It's never just "a few dollars" because
the amount in the channel needs to be
much greater than the fees
Your solution is to centralized transactions on a few large payment processor nodes?
The core problem of LN remains, which is that in order to operate a LN node you must keep it always online or risk having your coins stolen. The entire point of creating a L2 network in the first place was because Bitcoin Core decided that scaling the base layer with larger blocks would harm decentralization by making it more difficult to operate a Bitcoin node. Well anyone who has ever operated a server can tell you that maintaining near 100% uptime is a much much higher technical bar than buying a larger hard drive.
The alternative for LN users if they don't want to operate their own LN node is to give up custody of their coins to someone who does operate a node, but this goes against the core premise of cryptocurrencies.
Connect to a node that processes a million dollars worth of transactions per day, without securing the channel on the other side and congratulations you've invented a bank (albeit fractional reserve spending is more difficult).
Not that that's a terrible thing, I mean it's better than most banks: I've used it before as a means to transfer money from exchange to exchange: it's competitive and has low fees compared to SWIFT. But the problem is that if people rely on some centralized payment processor you will eventually get vendor lock-in.
You have that now with Coinbase commerce: before it was the case that they would just give you an address and you could pay with LTC or whatever, now they want you to download an app and link it with their system. That's the direction all this LN stuff is generally going.
If you go offline for a week, you can't
receive transactions for a week.
you've invented a bank
But I think the better comparison when it comes to the LN is Visa, not a bank. And again, there are many differences. One is that Visa can reverse transactions. Making payments costly for vendors because of fraud. LN nodes can't.