The manufacturer has mentioned to use "x-wattage" they know what they're doing. They have superior knowledge and pass it on. Even though it works for now, sooner or later it will bite you. Should the PSU fail, you will have problems, so best to follow what's recommended.
Recommended PSU is best for continued operation of the PC. NO, it won't make the PC run better but it will run which is the point for the recommendation for GPU operation. More demanding GPU tend to tax the PSU once its gets into more extreme setting or prolonged usage.