Truth told gain structure involves more than the console alone: the capabilities of a companion speaker system plays a critical role in the need to push input gain at the console. When a, similar to the CQ desk, budget friendly speaker system is deployed at a noisy gig nothing beneficial can come from it.
Unfortunately this conundrum is prevalent with many start up bands and acceptance of the fact that their role of providing elevator music is impossible to overcome with additional DBs: be an increase from either the desk or more powerful speakers.
The amount of speaker delivery power needs to be calibrated with a given venue’s nomenclature and adjusted pursuant to need with the speakers: never beyond the optimum gain level set at the console!
Hugh
You should never “push input gain” in a effort to increase the output gain because your speaker system isn’t up to the task IMHO. If you need to add gain somewhere in the signal process for this situation, it should be done at the output stage, not the input stage.