Hybrid precoders, consisting of an analog hardware-constrained part operating at radio frequency (RF) and a digital part operating at baseband, reduce the RF implementation complexity and power consumption of multi-antenna transceivers, at the expense of some rate loss compared to an all-digital precoder. The analog and digital parts of the hybrid precoder are commonly designed by performing a constrained matrix decomposition (MD) of the all-digital precoder, which aims to minimize the Euclidean distance between the matrices corresponding to the hybrid and the all-digital precoder. In contrast, in this contribution we determine the zero-forcing (ZF) hybrid precoder that directly maximizes the weighted sumrate of a MU-MISO-OFDM communication system, taking into account various hardware constraints on the analog part. The resulting maximum rate serves as a useful benchmark for comparison with other ZF hybrid precoders. In a multi-carrier massive MIMO scenario, the rate-maximizing ZF precoders show a considerable performance advantage over MD-type hybrid precoders, indicating that the latter precoders are far from optimum. This contribution also investigates the trade-off between performance and computational complexity. Because of the iterative nature of the rate-maximizing ZF hybrid precoders, their superior performance comes with a large computational complexity. When this complexity cannot be afforded, one should revert to the MD-type precoders, at the expense of a considerable performance penalty; among the MD-type precoders, the non-iterative ones have only a slightly worse performance but a significantly smaller computational complexity, in comparison with the iterative ones.