pallet-transaction-payment has ChargeTransactionPayment that implements SignedExtension. In its code, both validate() and pre_dispatch() call withdraw_fee() internally.
Why doesn't this cause multiple withdrawals?
Also, validate() could be called many times.
https://github.com/paritytech/substrate/blob/v2.0.0/frame/transaction-payment/src/lib.rs#L511-L534
Why doesn't this cause multiple withdrawals?
During validation phase, all state changes are discarded. Validation phase in used while the transaction lives in the pool. While being authored and imported, it only goes through pre_dispatch.
Also, validate() could be called many times.
Indeed, the pool (or generally any component outside of the runtime) might want to re-validate the transaction multiple times. Key is to remember that the state changes are discarded in validation.
See more here: https://github.com/paritytech/substrate/blob/a200cdb93c6af5763b9c7bf313fa708764ac88ca/primitives/runtime/src/traits.rs#L711-L728