you need to constantly have your
lightning node running to service the channel
Why do you think so? What do you think would happen when you go offline for a week?
It's never just "a few dollars" because
the amount in the channel needs to be
much greater than the fees
Connect to a node that processes a million dollars worth of transactions per day, then the amount in your channel is just "a few dollars" for them, for which they would not risk their reputation.
> Connect to a node that processes a million dollars worth of transactions per day
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.
If you go offline for a week, you can't receive transactions for a week.
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.
Same with the cash wallet in my pocket. I have to take it out to receive transactions. Not a problem for an individual. And for a merchant it is not a problem to have the wallet online all the time, or during business hours.
you've invented a bank
There are many differences. One is that the bank can see where you send money to. A LN node can't.
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.