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Right to know? Hell no.
Sure, I'll be more inclined to support merchants who are likely to keep sats over those who don't. But it's only one of many factors.
I want to support a bitcoin circular economy, but i don't want to enrich an exchange
The premise is a bit off. You're not enriching the exchange, the merchant does. Even so, I prefer being party to enriching an exchange over using fiat more than absolutely necessary.