I was going to sell some bitcoin in the next few days, and I gave my client my binance address. He immediately asked if I could be paid in BEP2 chain (Binance chain, using a BTC pegged token). I accepted, as it is a free and instant transaction and I was not going to hold that bitcoin for long.
Now, is a BTC pegged token bitcoin? It is not, but i guess it is useful for bitcoin adoption and awareness.
So, to summarize: Off-chain solutions are already happening. They are useful. LN is the best off-chain solution, but people do use it all the time yet. LN would be good for my transaction? Well, I think not as good as the BEP2 solution, but it would work.
That is a terrible and irrelevant example.
Binance chain has nothing to do with bitcoin at all, there is not even a weak link between the two chains. Binance chain is a completely centralized chain that is 100% controlled and owned by Binance. If some day Binance vanishes (like when government shuts them for money laundering), the Binance chain vanishes too alongside any tokens you had there or your balance in your Binance account.
In comparison LN is not only directly linked to bitcoin, it relies on bitcoin. Nobody can shut down LN since it is a completely decentralized layer without any central authority.
Additionally in order to transact in LN you don't need to convert your bitcoins to another coin with an exchange rate (even if it is 1:1 rate), you directly open your channel and enter this second layer. But in order to transact in another chain like Binance you have to convert your bitcoins to and from that token with an exchange rate that may change in the future. For example they may pay you 1 bitcoin for every 10 binancebitcoin you had. Just as they can print more tokens on that chain since there is nothing stopping them from doing so.