Every thread on SE and in general recommends a TTL flash for nightclub
photography. From my understanding, the only real benefit of it is,
that you have to chimp less often.
Think of it like using aperture-priority on the camera to adjust shutter speed based on metering. TTL does the same for your flash power. Chimping less often is good, but in an event situation, you may not have the time to adjust and reshoot. A performance or event has moments, and they may only be split second opportunities for you to catch it. (Say, like at weddings, the first kiss, the first dance, or blowing out the candles on the cake at a birthday). Chimping won't help you get that shot.
While TTL may not be perfect, it can be in the ballpark enough that it makes the difference between getting the shot or missing it.
But provided the club has even lighting and you don't alter your
settings, couldn't the job be do-able with a manual flash as well?
Well, sure, just as you can shoot things in focus without autofocus. It's just that your keeper rate may not be as high, you might not be as fast as the automated system, and your skillz/reflexes have to be very well honed.
Is there anything else I am missing?
The amount of flash exposure you get is dependent on your iso, aperture, flash-to-subject distance, and flash power. And the amount of light you can get out of your flash also depends on whether you're in HSS, a modifier you use, and how far you're spreading out the light (zoom). If you adjust any of these factors, you need to adjust your flash power if you want to keep the same level of flash illumination.
Changing your bounce surface (i.e., adjusting the swivel/tilt on the head), changing your position, having your subject move, using a higher-than-sync shutter speed, these all can require power adjustments to the flash to maintain the same level of light. Set and forget and bang away is only going to work if the ambient doesn't change, you never move, your subject never moves, you stay under sync speed, and use the same focal length/FoV all the time.
TTL can do this automatically; the way that using shutter priority or aperture priority may not be 100% exactly what you want first time every time, but will typically be in the ballpark. And just as you can adjust automated aperture/shutter settings with exposure compensation, you can use TTL with flash exposure compensation, and it would likely still be faster for most shooters than chimp-adjust-reshoot with M flash. Maybe you can just eyeball the light and know the flash power you need to use first time every time. But having a TTL-capable flash typically means you also have M mode, so you have a choice.