The important thing to understand about Lightning is that when all transactions happen off-chain, miners don't generate fee revenue.
This is where you wrong. Not all transactions will happen off-chain. LN isn't forcing anyone to use it, and it doesn't directly affect the base layer, so people will still be using it.
Exactly. Transactions of high amounts will probably go directly on chain as they go now.
Additionally, the once the channel is closed, the total amount transacted in LN will be registered on chain as well.