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Using Liquid cross chain with LN (onion routing) solves those issues.
Not really. LN changes nothing about traceability on Liquid itself. And at that point you might as well get rid of Liquid and just use Lightning.
There is no way you can have both "hidden amounts" and "provable supply cap". The entire reason Liquid opted not to hide amounts was to avoid this issue.
Liquid does hide amounts
In fact, a legitimate website or company would be barred from accepting monero because of the regulatory risk involved
There's plenty of legitimate white market businesses that accept Monero like Coincards, Mullvad, Silent Link, etc. Too many to even list: https://monerica.com/
The entire benefit of Liquid+LN combo is that you have gained the confidential aspects but are still using the most widely accepted form of crypto
How many businesses accept Liquid? Nearly zero. And lightning is nowhere near as accepted as on-chain Bitcoin.