The silliness and predictability of 14 CON point-buy peeps across all classes DOES need to end lol. And I think you identified a good example of the problem - that small HD classes (like the sulky Rogue you mention) get a lot of bang for their buck w/CON - proportionately more in fact than do martial types. Intuitively, this seems the opposite of "reality." But your solution hits all classes equally and therefore still leaves squishies w/their advantage.Currently, a level 10 rogue (bard, etc) would have around 55 hp with a +0 con bonus. This rises (obviously) by +20 with a +2 con bonus.
Now, that represents a whopping 35% increase. That's a huge bonus to the character's staying power, easily encompassing two full levels worth. And hit points is the premier indicator of level and power in this edition.
That's your problem and solution right there.
Make a Constitution increase from 10 to 14 impact your hp total by less than two levels, or an increase of over a third. And you should see players making other choices.
Mostly, I'm tossing ideas out there. I'm tired of Con being everyone's second or third choice. It's boring. It's a non-choice. There are other ways to solve it (I'm a huge fan of 4E's Con mod to healing surges).
What are your thoughts on Con?
What's a "tier" in the context of 5E?13th Age adds Con mod to HPs once per tier of play instead of once per level. That might be an easy yoink. CON would still be important in 5e because it adds to spending HD.
Delineated by the shading on the Character Advancement chart, and explained on the same page (15) in the PHB.What's a "tier" in the context of 5E?
What's a "tier" in the context of 5E?
3) Cool. Right up until one of the slew of monsters with darkvision spots you. Better hope you’re a dex fighter too, else you really like that disadvantage for heavy armor.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.