The more you use Lightning and the more channels you have open, the greater the potential savings on fees. Each time you can avoid making on-chain transactions, that's one less mining fee to pay.
But each time you open a channel you pay the on-chain fee, which would be very steep if bitcoin would ever become popular. So I just don't see people opening tons of channels and put a lot of money in each and every channel. That just makes no sense.
Lightning opens up two new choices for how to transact. Opening a new channel, or routing through one of your existing open channels. If this scenario of no sufficiently funded channels occurs, you might not be able to route through an existing channel, true enough. So you open a new channel. Or you send a regular on-chain transaction. Not exactly rocket science. Plus, that's still more options overall than you previously had, so if one of the two new choices isn't available, that doesn't constitute a failure.
The thing is, you compare it to the on-chain form of bitcoin. But that makes no sense, that's a failure already. You need to compare it to VISA for example.
You've effectively countered your own point. The sense in people paying the fee to open a channel rather than just making an on-chain transaction, is that it
that Visa level of scaling. Once a channel is open, there is no limit to the number of transactions you can make as long as you still have adequate funds. You don't have to wait for however long the next block might take to be found. You also don't have to worry about working out what mining fee would get your transaction confirmed the fastest, because none of that applies. You don't need to wait for X number of confirmations. Channels are also bi-directional, so the funds don't just have to go one way. Those are all reasons to have channels open and funded, ready to go.