Many recipes call for an egg and a white (or yolk) since it better approximates that scaling. Or if you double it, it becomes 3 eggs instead

I always doubled "an egg and a white" as "two eggs and two whites". Whites and yolks are very different and make the end result very different.

Eggs can be considered continuous with a large enough volume of them.

Also you totally can reduce an egg by 30%, it's just a pain in the ass.

Separate yolk and white (as though you were going to beat the whites). Weigh both, reduce both by 30%. Recombine.

Better is to just base the entire recipe off the weight of the egg.

Start with the egg(s), scale everything else to match. 50g egg? Cool you get even increments of 50g, 100g, etc. 48g egg? Weigh out 96g instead of 100g of the other ingredient.

Why separate, split, and then combine? Why not combine and then split?

I am guessing: unless you blast them in a blender, the beaten mix isn't really uniform and you may end up extracting more egg white or more yolk than intended when you remove some of this lumpy content.

^ yea pretty much this

I'm not 100% sure but whenever I've tried to reduce an egg without splitting first, it always ends up with a super wrong amount of yolk

I could also just be bad at it, idk

At that point you may as well start worrying about the variance of the yolk to egg white ratio in different eggs.

In many recipes you must whip the whites, and they must be completely yolk free.

This is a useful thing to know when writing instructions on how to bake 1000 Betty Crocker cakes

Sure you can. Scramble them a bit and weigh them.

Grocery stores sell different sizes of eggs over here.

You can just buy small eggs, and use them for fractional eggs.

What about liquid egg whites/yolks? Aside from the shelf life this always seemed like a key selling point to me.

You're cake is going to turn out fine with a bit more or less egg in it. Just adjust other liquids a bit to compensate.