Here is an example. Is better than ±1°C when measuring ambient air temperature in a commercial office required?
A Building Manager might be happy with an accuracy of ±1°C and a resolution of 0.5°C, while a Scientist researching indoor air quality in the same office might want an accuracy of ±0.3°C and a resolution of 0.1°C. So potentially yes, some applications will warrant better than good accuracy.
Resolution is also balanced around accuracy. Just because a temperature data logger can display down to one decimal place (Resolution), that does NOT mean the Accuracy is as good. You can have good Resolution without the Accuracy!
More about Accuracy,
Resolution and Precision