Nope , you are wrong . If someone has enough liquidity can transact infinitely in LN without closing it's channel/s . In what way that person supports the miners ? On the contrary , with a very small investment , LN nodes work like parasites that suck fees from the true backbone of the system , that has cost billions of investment . Imagine if all transactions move to LN , and miners just wait to be paid from opening and closing channel fees . How would that be sustainable ?
That will never happen.
It will take decades to open channels for 8 billion people (assuming all transactions are LN-related, which they aren't, since we also have Ordinals and other stuff).
Besides, BTC uses a free market system to determine fees:
https://mempool.space/If fees drop again to 4 cents per TX (it happened a few months ago), who's going to use LN compared to on-chain?
It's a self-regulating system (just like the hashing difficulty). There's nothing to worry about.