You can, but I suspect that the typical user won't bother. Only time will tell.
Interesting observation, but I see a problem here, when these exchanges goes down. We will have a single point of failure, if the backbone of this system is built on a network of centralized hubs.
The exchanges will in a way function as centralized payment processors and if we have to rely on centralized authorities to "channel" our payments, then we are moving away from the original idea behind Bitcoin being P2P.
It's not that LN REQUIRES the exchanges to be hubs. It's just that when I look at how it works, that currently feels like the most likely growth pattern.
If you receive your purchased bitcoins over a lightning channel that the exchange set up with you when you open your account with them, then you can spend those bitcoins through that channel for free (or extremely cheap). If you want to open a new channel with someone else, then you'll need a new on-chain transaction. This will require you to pay a on-chain transaction fee to open the channel. Why would the typical user pay fees of multiple dollars to open a channel with anyone else when they can just send them bitcoins already very cheap?
If the exchange goes down, then the user can pay an on-chain transaction fee to close the channel, then pay another on-chain transaction fee to open a new channel elsewhere, and then they'll be able to spend those bitcoins again, but there's a good chance they may only bother doing that once. Again, why pay transaction fees to open multiple channels when a single channel to a well connected and well funded entity will be sufficient 99.99% of the time?
There will be some users that will open multiple channels with non-hub partners. Those will probably be the same people that currently run FULL nodes. But I figure there will be 3 major types of users:
1. Knowledgeable, and technically capable users that want to maintain a decentralized system and connect to many non-hub channel partners.
2. Those that hear they shouldn't leave their bitcoins in an "account" with a third-party service providers, and set up a lightning enabled wallet. They make withdrawals from exchanges and then they make payments. They may not even realize that all their payments are routing through the single exchange channel.
3. The vast majortiy of users that don't understand the difference between a "wallet" and an "account". They just leave their bitcoins in their account at the exchange (or some other web service) and spend them directly from there.