What would happen if in the Foster Care System, Kids were kept at ONE foster-family instead of house-hopping?

I’m writing a pretend-bill in Civics, and I decided to do something about improving foster-care. Many critiques of the system we have now say that for children (Usually older kids) who aren’t adopted and surf through the adoption/foster-system for years are constantly uprooted from foster-home to foster-home. I would assume that this creates an unstable environment for the kid or teen in question, and I was wondering what major consequences would be for those children, if they were assigned to a single foster-home?

I understand that foster homes are supposed to be temporary, but for people at that impressionable age to have such little, “grounding” in their life and surroundings, how could it be beneficial?

Problems I’ve thought of so far are:
-the children become too attatched to a family, and the family in question is unable to adopt, causing emotional pain.

-Kids might not “fit” into the family unit chosen for them/the foster-parents wouldn’t be able to handle the emotional/behavioral baggage associated with the child

But good things I’ve thought of are:
-Older kids and teens can have a stable home and not worry about being yanked out of it and thrust into a different house with strangers.

-Older kids and teens would be provided with role models who can encourage them and give them support in a way that other temporary families and counselors cannot.

Etc. Etc.

So, if anyone has any information or ideas, or better-understanding of the current system we have now, please reply! Thank you!