You are remembering wrong.
The Covenant Campaigns in Shadowlands required you to dungeons. Not many, but some. But those campaigns didn’t start until you had reached max.
Or are you talking about levelling your character? You should be able to get through Legion and BfA levelling storyline without dungeons - and certainly without raids! - AFAIR.
If you are laking about doing the level-cap campaigns for each expansion while your character is levelling, the game has no intention that you should do that.
There are no Follower Dungeons below Dragonflight.