Why is there a 2 step heating process for making custard for ice cream
These steps are done to ensure that the custard in the end is the best it can be. The best custard has a smooth, and creamy consistency.

Warming the milk/cream with the sugar will ensure that the dairy and sugar are completely incorporated. This could be done with cold dairy, but you would have a higher likelihood of having sugar granules that do not dissolve, heading toward a gritty custard.

Whipping the yolks and sugar to a pale yellow does a similar thing. Well incorporated ingredients will be a recurring theme here.

Step 3 and 4 are more related than one might think. Step 3 is the first step in incorporating the diary and the egg mixture. By adding part of the warm dairy to the egg mixture, you are tempering the egg mixture. This means you are bring the temperature of the egg mixture a little closer to the temperature of the dairy. So, when you add the rest of the dairy to the egg mixture it won’t cook the eggs, leaving you with a lumpy, or grainy custard. If you were to add all the warm dairy right into the egg mixture up front, you may end up with a large amount of very sweet scrambled eggs. Not that appealing, really.

You already know that part since you mentioned it in the question; just trying to be thorough. 

Step 5 cooks the custard. Since we are dealing with eggs, we want a minimum temperature: 155/160F. You don’t want to go any higher, though (sweet scramble eggs).

As you already know from experience, following these steps will give you great results every time.

To answer your final question… 

You could just put all ingredients together and come up with a decent custard, and that would probably work when dealing with small batches. It could be worth experimenting with. If you are like me when it comes to baking, or delicate cooking… if it isn’t broke, don’t fix it.

Time wise, it may take a little longer. The reason I say that is because, in my experience, when you do the steps separately, you can do a couple steps in parallel. You can whip the yolks and sugar while the milk/cream and sugar come up to temperature. Also, you may be starting with a cooler mixture when you start to bring everything up to temperature if you do this all at once, that could slow you down a bit. Not that there is a race. But, if you are a professional cook, time may be a consideration.

Why did I mention this could work for small batches? Well, I have made custard in larger batches (3 to 5 gallons), and I just don’t think that doing it all at once would be any fun at all. Stirring 5 gallons of already mixed custard batter until it comes to temp seems like it would take forever, and almost guarantees I end up scorching something. There is some fun in preparation, but that is pushing it a bit. The recipe you have may have been adapted from somewhere they were typically worked in large batches (total guess on my part). 

I think I covered everything. Hope this helps you!