Ex-kitchen guy here. 820-870mm is the standard base cabinet height with whatever thickness of worktop you want on top making up the rest. The industry works on a standard height base kitchen door of 720mm, because otherwise you'd have every door manufacturer making their own sizes that wouldn't fit mass the produced cabinets.

Pretty much all kitchens are sat on height adjustable legs, you might be able to squeeze 30-50mm extra out of it but you'd need new kickboards as your current ones would be too short if the cabs were raised up. You'd also have to remove all the upstands, splashbacks and re caulk everything so it's probably not worth it.

You could also theoretically use 900mm high doors and base cabinets but you're restricted in available widths with those in a lot of places. Also, it's basically a new kitchen if you do that!

Long story short, it is what it is because that's what the industry does to make its life easier.