Metatransactions have many advantages over a faucet:
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Existence is more obvious, you wouldn’t know about the faucet unless you google it / a DEX integrates it into their UI
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UX is closer to TradFi
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The fees are ultimately paid for by the user, just in a different currency (?)
Though I don’t know enough about the mechanism to make a proposal. Maybe someone with more knowledge has ideas on that.