How does it solve the problem in any way?

If we take a step back, we should also realize that no other cryptocurrency has this problem. You just let the throughput be higher and it works, because 1 KB/s is completely absurd in 2023.

Any transaction still has to make it on to the chain. A side chain would be like us playing catch in the back yard and thinking we will somehow be padding our major league baseball stats. It doesn't matter until something happens where it counts.

If you find someone to play catch with, that's great, but the whole point of a global transaction network is that anyone can send a balance to anyone else.

Lightning has a fundamental graph theory / routing problem. As the number of nodes increase the path between those nodes grows at a nonlinear rate. The internet has this problem too, which it mainly solves by letting a human put a finger on the scale in a centralized fashion. Lightning network cannot make this tradeoff. It's a simple mathematical problem that we've known about for centuries and it's baffling that anyone thought it would help in the first place.