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Recent advances in quantum computing pose a looming threat to most current Byzantine fault-tolerant (BFT) consensus protocols, which rely on quantum-vulnerable public-key signature schemes such as Ed25519 and BLS12-381. Instead of switching to much more expensive post-quantum secure signature schemes, an alternative is to use signature-free protocols, which rely only on cheap, post-quantum secure authenticated channels. In this paper, we ask whether signature-free BFT consensus protocols can match the performance of current state-of-the-art, quantum-vulnerable BFT consensus protocols. While previous work on the Sailfish++ protocol showed that state-of-the-art throughput is attainable signature-free, the question of latency is still open. Several recent signature-free protocols have low latency in theory, but they are all very intricate, and no practical implementation has so far been presented. In this work, we propose Simple-IT, a new leader-based, signature-free BFT consensus protocol that achieves a theoretical latency of 4 message delays (one more than the optimum), and only 3 on its optimistic path. Crucially, Simple-IT is simple enough to be amenable to implementation and to practical optimizations such as speculative pipelining, and, as we show experimentally in a geo-distributed testbed, it achieves both throughput and latency competitive with state-of-the-art quantum-vulnerable protocols.