Specifically wrt to privacy, there are pitfalls and subtleties in using Lightning Network privately but it is doable. I think this article does a good job summarizing the current state [0].
IMO LN is secure enough to sleep well at night with open channels but you definitely want uptime monitoring and at least one watchtower hosted on separate infrastructure from the LN node, or great trust in whatever custodial wallet provider you may be using to not doxx you if you do and that's a concern. (Seriously though, any cryptocurrency going through any form of custodianship with any form of company/business will eventually have to be KYC’d and accounted for to authorities, if currently existing and planned regulations take effect. Self-custody and, for L2 like LN, self-hosting, takes some self-education but is the only way to get the true benefits of cryptocurrencies)
"Solution" because it does not actaully allow fast and cheap "cash-like" transactions as Bitcoin was originally designed to do (and still can easily scale to Visa-like levels).
From day one Satoshi had built Bitcoin to scale to to Visa levels of transactions by simply incrementaly increasing the block size over time. Blockstream hijacked the Bitcoin Core GitHub repo and soon after disabled several core features and have since refused to increase the block size while pushing their products (Liquid and LN) as "solutions" to this problem they created.