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User Experience

Wallet software should warn users about the dust limit when creating small UTXOs. "Funds will not be spendable in high-fee environments".
This is equivalent to the central bank deciding to expire old coins or notes. In fiat it's done because of inflation and other reasons, but Bitcoin is not static either. It needs to be communicated clearly, and wallets haven't had a real fee market to deal with for a few years.

Attempting to switch to lightning

There is talk of supporting hardware wallets for lightning, BitBox-guys are prototyping something with Greenlight, but I'm not aware of a finished solution.
Lightning isn't built for offline/cold storage. The protocol assumes you will have a lightning node or watchtower that monitors the blockchain to see if the other channel party tries to cheat by publishing an old channel balance, so that your node publish a second transaction to counter it. Channels are based on 2of2 multisigs and transactions spending from them must be signed by both parties, so if the only channel states that exist are with the significant majority of the balance on your side, then you should be fairly okay, unless one side's node software decides to force-close the channel for some reason, and spends most of the balance in on-chain fees.
You could use Blixt & Dunder LSP with what others have claimed to be hosted channels. Sounds semi-custodial if this is the same kind of hosted channels I've read about before. Basically the LSP could rug you and you end up holding a "proof of rug" and no sats unless you take it to the courts or something. Haven't looked deeper into this yet, could be wrong.