I make my morning coffee on a Lelit espresso machine. I use a Niche zero espresso grinder. I can easily tell the difference between grind sizes a mm apart on the dial, when it comes to taste in the cup (and even with milk). The espresso machine can tell the difference too, because even a minute difference in grind size can make a significant difference in the coffee puck’s ability to withstand the water pressure.
You see, when you make espresso there’s a pretty narrow range of grind sizes that produce acceptable coffee. Too coarse, and the water gushes through the puck without building much pressure. Too fine, and the puck essentially turns into coffee cement and the machine isn’t able to squeeze out more than a drop or two of (very bitter) espresso.
Within that narrow range you can find the needle on the water pressure gauge hitting numbers anywhere between 4 and 10 bar (I’ve set my machine’s overpressure valve to 10 bar so that excess water pressure is shunted away and circulated back into the brew circuit). I find the coffee tastes best when I can hit the sweet spot between 9 and 10 bar without the OPV kicking in. This is subject to uncontrollable factors such as differences in tamping but generally occurs at a very specific grind setting that I find after dialing in a new coffee.
As for differences in flavour? It’s all about extraction. Underextraction (from failure to reach a high enough pressure) results in sour, thin coffee. Overextraction yields very dark, bitter coffee with a powdery mouth feel. Proper extraction avoids both of these problems and tastes sublime, nutty and chocolatey (with medium-dark roasts) or fruity and juicy (with lighter roasts).
There may be a lot of gadget-headery going on in the espresso world but I can confidently say that correct grind size makes an enormous difference in the quality of coffee. Whether you need a $2000 grinder to achieve that is debatable, but you absolutely will not achieve it with a $40 blade grinder (which cannot control grind sizes at all).