A tachometer on an automatic transmission vehicle can be very useful, especially for one that is electronically controlled.
If I want to get the transmission to shift smoothly at something like 3000 rpm in each gear, I can gradually accelerate and then let off the throttle just a bit as the tachmeter nearly reaches 3000 rpm, at which time, the transmission will shift at the desired RPM's.
Same goes for if I want the transmission to shift at 2500 RPM's or less (although that's really slow acceleration generally only used in residential areas) or at 4000 RPM's or more (climbing a bit of a grade). The accurate shifts at a given RPM can continue to occur until the transmission reaches its final gear and torque converter lockup subseqently occurs, thanks to the visual feedback of the tachometer.
After a while, I've learned the acceleration rates for shifting at a given RPM, so I can maintain the throttle in a constant position such that the transmission shifts smoothly at the desired RPM.
Without a tachometer, I could judge by engine sound, but not know the exact RPM's. And, it's also helpful to know when the engine is approaching redline under more spritied acceleration (e.g., flooring it on a very short interstate onramp that merges rather than joins with an extra lane, giving very little distance to get up to the 65mph freeway speed) rather than just waiting for the transmission to automatically shift to the next gear when the engine hits redline.
Since my car's specifications indicate a maximum of 126 horsepower at 5500 RPM, there's really no need to exceed 5500 RPM, but I wouldn't know if I reached or exceeded that max engine torque RPM under higher acceleration without a tachometer.
Others may vary in their usage or requirements for a tachometer.
