Cashu uses Lightning. If Lightning doesn't scale then Cashu doesn't either.

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Lightning uses Bitcoin. If Bitcoin doesn't scale then Lightning doesn't either.

Is every Lightning transaction likely to be a Bitcoin transaction?

Nope. Nor is every Cashu transaction likely to be a lightning transaction.

Why not? Are you operating under the assumption that most people will use the same mint?

Not most people around 1 mint, but groups of people around common mint. The incentives suggest so.

One Lightning channel can serve millions of people though.

How about billions?