I think this is at the nub of it. We think in terms of CLUBS, not TEAMS, esp in rugby & cricket
If we take rugby as an example, my understanding is that in the UK a clubs 1st, 2nd and 3rd XV's are pretty much seperate entities who play in different leagues against different opposition. In this case team pro/rel is possible.
Here we play as clubs. So for example Second Division clubs City and United will play. Their 3rd XV's will play each other at 12 noon, followed by 2nds at 1.30pm, followed by 1sts at 3pm. Players from lower grades will sit on the bench for higher grades
If City's 2nds win their premiership at the end of the year they cant be promoted, as there is nowhere to promote them to. City already have a team in First Grade. Just say City win the First Grade premiership - promote them to First Division you say, but what the Union will look at is how competitive their 2nd and 3rd grade teams are as well, as all three teams will need to go up to First Division.
If my 6th Division team was promoted to 5th Division, then the 5th Division clubs 2nd XV's would have no one to play against each week.
A couple of years ago we were actually invited to go up to 3rd Division and to play in the 4th grade slot of another club that was anticipated to be struggling for numbers. We declined as (a) we would have to play at 11am, (b) We would smash 3rd Division 4th Grade teams and (c) we would never have home games as the opposition clubs wouldn't agree to send 3 teams to one clubs ground and 1 team to our ground
And of course pro/elite leagues are closed shops. In the case of rugby league and aussie rules their "reserves" teams generally play in the state leagues, often under different names - like the US baseball "farm" system