I'm the oldest of 6 children. Our ages are 22, 20, 20, (twins) 17, 11, and almost-7.
I think the hoarding you've described and the competing for attention are a result of bad parenting more than too many kids.
We definitely had some very very tight years financially when I was a kid. One year my dad made 14k. That was when there were 5 kids. My parents were very very good at budgeting though, and I never realized until I was almost 18 how much they had struggled. We had a vegetable garden and were allowed all the raw veggies we could eat, any time of day, and there was always plenty of other food at meals. Sure we'd fight over snacks and stuff. At one point my dad bought a scale for dishing up the ice cream so each child got EXACTLY 6 oz so we wouldn't fight about who had more.
I think one reason we didn't hoard was that my parents always put an emphasis on personal property. Andrew's toy was Andrew's, and nobody else touched it without asking him. So even if we didn't have much, the things we had were OURS.
I don't recall competing for attention either. My mom was a SAHM and EBF all of us, my sister BF to 4 years. My dad worked at home almost my whole childhood. We homeschooled for a few years, I did for 4, 5, and 6 grade. We did a LOT as a family, we were always going to parks, zoos, museums, etc. When at home we were always doing crafty projects and reading books.
I think a big family can be a really good thing. It's not always, but in my case I'm glad I grew up where I did.
