Lightning network helps repeated small transactions between the same pair.

However, the first transaction between a specific pair (channel opening) still needs to occur on-chain. That transaction still pays a full fee.

You can route through your pair. Say A has a channel with B, B has a channel with C and C has a channel with D, you can make payment between A and D provided that B and C are online. In a way that nobody can steal money from one another, and neither B not D know who is paying who. In practice, B and C would probably be like banks or exchanges, with many channels, while normal users only need one channel open.

True, and in fact lightning payments tend to take many hops if routed publically.

But every citizen would still need atleast one lightning channel. And opening those is expensive.

The lightning channel would go through a custodial wallet. Yes, people could self host their own wallets, but fees would be higher because they'd have to open a lightning channel.

So you need something centralized for it to actually work.

No, why? It's all P2P.

How secure is it compared to real transactions?

There are risks, you need to remain online to catch your counter-party cheating. There are ways to outsource this to so-called watchtowers. This can generally be done privately, and the watchtowers generally get to take at least some of the cheater's money.

I haven't heard of any successful malicious channel theft. I have read quite a few stories of people losing local data making it much harder to recover the money in the channel.

As far as I know you have to be on the internet at least once in 30 days, so it's good only for hot wallets. Also for payments over $1k probably right now Bitcoin transaction is more practical (I have heard of $100k lightning transactions though).