You are close to the idea but very far. Each class is leveled up separate depending on how you want to make your character as he levels up, like how a lv12 human can be lv8 druid, and a lv4 monk. What I'm getting at is the same concept, but you only get the basic features once.
Ok so you said 3 archtypes well that means there are four tables. The main and three archtypes. you can only get the abilities from each of them once so the main table can only be done once, so say you have a lv7 druid circle of the land who is also lv 5 in circle of the moon. he only gets up to level 7 on the main table but get his 12d8+con hp and get the befits of his circles at the same time.
As for stopping at level 20, you're right when it comes down to just the first arche type but if you wanted to master it you would need to be level 17 to get the first archtype done, then level 34 for the second, and 51 for the third, and another 3 for the main table this bring you to level 54, and now you can say that you mastered the class.
And just to make this clear. if you think this is nuts. it is. your dm will have to constantly modify the baddies and goals even be unfair, but as it says in the monster manual those are "base stats"