Association football ran an elected league system for decades till it grew so financially and numerically massive it could afford standards based P/R across 11 tiers of ever increasing numbers. It doesn't have its equivalents of Hunslet or Swinton anywhere near its equivalents of Southampton or Hull City.
Cricket has quite literally a major counties only league. The second division being introduced to split the number of red ball matches being played by those special 18 counties who otherwise all compete on the same level.
Union only went pro and had "proper" leagues in the relatively recent past. Even then, in England it is heading to a closed top/top 2 tiers - In Wales, Scotland and Ireland it already is like that.
Rugby League is the prime example of a competition set up specifically for one type of club, "professionals"! We've never had a "pyramid" because we've always had a clear distinction between the amateur and "professional" clubs. For the past 25 years, if not the past 35 years, the sport has grappled with whether there should be a distinction between the fully professional and semi professional levels too.