Sure there is inheritance in the wild, it’s called eusociality. Any animal group that holds territory fights to hold it and passes on that territory to their offspring. “Each new generation of animals starts from the same place” is definitely a romanticization of how non-human animal society works. Lion prides fight for the best hunting territory, leaving the weaker group to starve in poorer territory. Same for wolves, same for most primates, and these are just the easy ones off the top of my head.

The original “old, dead animal” that took the prime territory in the first place continues to control all the territory because his offspring and family group get the most resources and have the advantage in fighting to defend it. The only reason there are no animal billionaires is because seasonal resource scarcity cannot be overcome without agriculture and ability to plan months or years in the future, which limits the size of a group and group interaction. Animals don’t stop expending territory because they hit an upper cap on their needs, they only stop at the limit of their ability to hold it.

I don’t know about you, but I think the modern human method is better than having to fight daily to hold onto my house and job, and that it is frowned upon to attack and drive off or kill the patriarch or matriarch of a family and take their place if you want to own instead of rent. The human method still needs lots of work because we still have those same animal desires to keep expanding territory.