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And the amount (balance) of the input doesn't make the transaction faster or slower, it's still the fee rate (sat/vB).
The issue with "smaller inputs" is a transaction might need more than 3 of them to fill the amount to be sent making the transaction's size higher,
the higher the transaction's size, the higher the total transaction fee based from the "fee-per-vbyte" will be.
[1] Clients will select the right input(s) that's enough to pay the receiver by default, not just spend random ones.