I totally load by section: big plates here, small there, glasses here, cups there.
The tighter packing is nice, but as you say it usually gets run before getting full.
IME having the items segregated by type adds nothing to the difficuly of loading but greatly speeds the unload and stow process.
That’s the payoff.
Part of the “duty splitting” in our house is my wife does the laundry and I put things away, including stacking the sheets in the linen closet and making our bed. It seems to me, the most logical way is for the top sheet pattern side to face the bottom fitted sheet so that when the top sheet is “folded back” you then see the pattern. At least that’s the way I’ve made the bed for the 37+ years we’ve been together and I’ve never been called on it.
As the topic was raised, I think I’ll comment on the toilet paper roll issue. Only my wife and I live in our house now, but we have 4 bathrooms. The one who uses the last of the toilet paper changes the roll. whenever my wife changes it she positions the roll so the paper hangs on the back nearest the wall and I hang it so the paper hangs outwards.
Buy solid color sheets. Then there is no top or bottom side.
I would prefer a pattern facing outwards. 
But it’s not something I’d mention. Whoever makes the bed can do it the way they like.
Our problem is how to fold towels. Different methods leaves a different shape. It looks odd in the linen closet with a stack of folded towels that aren’t the same.
That’s not necessarily true.
The fabric itself often has a more-finished and a less-finished side. One is notably smoother than the other. The difference comes from the process by which the cloth is woven. For patterned sheets, they’ll dye the pattern such that the smooth(er) side of the fabric has the face of the pattern and the rough(er) side has the reverse of the pattern.
The difference can be subtle. But it’s not zero. At least on some sheets.
Exactly, I tell everyone I, “reload,” i.e. rearrange the dishwasher after I, “load” it. It depends a lot on what was in there originally and what needs to be added.
I do that too. I try to keep like items together* for ease of putting away, but efficient space usage is higher priority.
We are on the same page.
Bath towels - Fold in half then in thirds
Kitchen towels - Fold in half then in half again
Face cloths and hand towels the same as kitchen towels
It would never occur to me to put the sheet on finished side down