The labels like "Warden" and so on are tenuous and arbitrary at best and deciding who fits where is splitting hairs.
I've noticed you've had people give examples like Thresh or Rell in the comments, only to have you say "They're not Wardens, they're XYZ", which I think misses the point.
As much as anything else, Warden is a playstyle, not a defining characteristic of a champion, beyond a kit that says "This champ can be played as a warden".
Leona, Maokai, Galio, Rell, Thresh, Poppy, Shen, etc.
Yes, some of these champs can "Engage", but all of them punish aggresive plays made against them. You dive a poppy or a leona and you suffer for it, you ignore a shen and you suffer for it. All of these champs can be played effectively in a defensive style, so too can the examples you've given be played aggressively (Taric ulting yi to initiate a teamfight, for example).
If there's something you think the game is missing, don't use buzz words; describe ...