The issue is call commit fees or the reservation for the fees when you close your channel.
This commit fee will increase as on-chain fees do.
So if you have a channel with a capacity of 0.001 and Bitcoin on-chain fees are 0.0005 that will mean you have lose 50% of your channel capacity. The reserve fee will or may even trigger node operators to close your channel because they know your channel can't cover a force close. It becomes risky for node operators to continue the contract with a channel that doesn't have the sats to cover the closing channel fees.
At $10,000 price you will only need to have a fee of $5 to lose half of your capacity and $10 for your channels to become useless.
Fees in the pass were $50 but because of segwit let say the highest a fee gets is $25 and Bitcoin price is $20,000 that will mean your commit fee will be 0.00125 btc. Meaning small channels will become useless.
Even at 0.01 capacity that is 10% on commit fee. So if fees continue to increase to make the opening and closing of a lightning network a worth case you will need to start creating channels with 0.05 or more.
ONCE AGAIN MAKING BITCOIN AND LIGHTNING NETWORK IMPOSSIBLE FOR THE LESS FORTUNATE. UNLESS THEY START USING CUSTODIAN SERVICES ONLY, WHICH DEFEATS THE WHOLE IDEA.