No I don't fully agree with your title. I will add I have no half siblings but I have had 6 step siblings in my life.
I was 5 when my parents parted. I went with our mother who moved in with her OM immediately (and stayed with him for 35 years until her death) sister age 12 and brother age 2 remained with dad.
Result was dad.focused on our brother as he needed him the most. Sister went into huge rebellion mode. Mother hugely.guilty always prioritised brother and sister. Dad remarried 1st time. Step sister aka spoilt brat became number one attention she didn't even live there full time. Had to have her own room. Decorated just so. I slept in the dump room. Old coats smelly stuff. I can remember being scared in the room and the old sofa I slept on was itchy.
When my little brother came to mums I had to share everything including my room and he didn't in dad's home.
Dad divorced remarried 2 new step siblings. Sister now a grown up in her own home. Brother and 2 step siblings had their own rooms I did not belong there.. I was a welcome visitor. But never once slept there. Stepmum no 3 was lovely however after their divorce she cut contact with us.
I grew up never feeling I was important to either of my parents. I'm the middle child.
My maternal grandmother saw this and gave me a lot of her time. This caused resentment from cousins and aunts/uncles.
My step grandparents were amazing my youngest is named after him for her mn. My one place I had unconditional love was with people whom I shared no biological blod with.
Dad remarried for the last time after I had children myself and had moved to the UK. she had2 children herself and technically I guess I have 2 stepsiblings. I've never met them. They keep in contact with our dad. His wife died many years ago.
Sister and brother are close to dad. I'm not. How could I become? There was no room in his life for me as I was growing up.
Mum was so guilty she spend my childhood dismissing me as "I had her" and made a big deal out of the other two. She died 9 years ago. It's rare I miss her.
My MIL on the other hand. She passed 4 years ago and I think about her daily.
So no OP. Idont think it's always the eldest. In fact in my case I think the oldest got the best of everyone as she was so clear about her needs they gave it to her.
I also know of families where the oldest children are considered thr golden ones and the next set second best.
I think mixed families are a mine field and its hard to get right for everyone.