It the generic problem that the typical melee classes don't actually get much more in the way of defence (usually just a couple of HP) than the 'squishy' classes. In fact, a quick dip for Medium Armour and Shield proficiency lets casters beat them on AC (the melee classes get punished for using a Shield, and of course then there are defensive spells, as well as being able to just Dodge while still being effective due to ongoing Concentration spells). The HP part is minor enough that a single low cost heal out of combat is the difference.
Moon Druids and Barbarians are the exception to this rule in 5e; Barbarians get resistance, and Moon Druids get chunks more health.
It is often considered that Fighters and Paladins are tanky, but that more visual idea than a mechanical one. The way to survive in 5e is to either kill the enemy fast, lock the enemy down with control, or to stay at ranged. Alternatively, have a Barbarian or Moon Druid out front absorbing hits if the DM plays ball.
The question for the D&DONE Moon Druid here is, what do they gain for going into Wild Shape, what do they lose, and does this pay off? It seems to be a little more damage is gained at the cost of being cast into melee while being fragile. I would rather just stay back and spam cantrips.