I completely disagree. I think the idea you posit here is completely out of left field.
The dwarf has higher con because dwarfs in general have higher con. PC, NPC, all that changes is the specific methodology used to get there. In both cases, the dwarf has higher Con because the definition of the dwarf people is the writeup in the phb. Obviously part of that writeup is the bonus to Con. If it wasn’t, we wouldn’t be having this discussion. The dwarf is, in part, defined by being hardier than other folk, which is represented primarily in D&D by their Con score.
not sure I see how this is even relevant?
I mean, they barely are. The disadvantage on attacks with heavy weapons is a vastly bigger hindrance to the halfling barbarian