1st off, Poppy Q does physical damage, which is easier to reduce generally.
2nd, Cho'Gath is weird because of how his ult functions. Full tank or full AP Cho'Gath can still kill you with that ult. But full AP Cho is building AP and health items like
and/or
(I'll admit I don't know Cho's common builds, but these are items I build on Galio so I just assume they share similar items). A lot of AP bruiser builds have this, and it's stronger on melee tanks because of their better base stats (though I don't consider this a bad thing. They aren't glass cannon like a full AP mage but they aren't as durable as a full tank due to not as much resistance. They are durable enough for some people though).
I don't think any tank has enough base damage to one shot a character at level 1 with the starting amount of AD/AP available. The %health damage on tanks is usually to help deal with more durable opponents in lane (and is generally weaker against squishy targets. 5% of 100 is less than 5% of 300). The large base damage obviously are threats to squishies, but the large base damage is more for farming than anything else, and because squishies are squishy, this means that even basic farming abilities can be a threat to them.
Now granted, I don't think %health damage on tanks should be reliable or be put in their primary trading ability. I'd much rather put all of Poppy's %health damage (both ticks are like, 14% total I think) on the second Q proc and just have the first one be flat damage, better rewarding her to landing her E stun to get both procs. But Riot doesn't do this, probably because it'd make her main trading ability too unreliable in lane. Sion's W IMO is the healthiest version of a %health damage ability, because you can break the shield before it explodes, negating the damage, or you can run away from Sion to avoid the explosion, also negating the damage. The best part is that it isn't his primary trading ability, so you won't be seeing it every time you trade (you'll see it a lot still, but less than his main trading ability). IMO it's much more healthy than Sejuani E proc or Cho'gaths E.
%health damage is also (at least I think it is) really weak against resistances. So getting some resistance boots or buying a resistance item can really help early if you are having issues with it.
So if this type of damage should be tweaked, it should be made more unreliable, with more counterplay.