It wouldn't 'break' anything really. Just so long as you still let rogues sneak attack undead/constructs without jumping through feat or alternate class feature hoops, it should be fine.

As Beelzebub said, the removal was mostly to streamline it for DMs - means you don't need to remember creature traits. They could have added those sorts of traits to every single statblock, but I'm guessing they didn't want to use all the ink+page space, so they only hit the high-notes when necessary.

Vulnerable being double damage is pretty potent though (and lopsided vs. Resistance, typically), especially when the numbers start getting bigger. If that's a concern, you could trade it out for something like
Radiant Weakness
The creature with this trait takes an additional 1d8 whenever they take Radiant damage.
But Vuln might work just fine too. No reason not to try it.