Worst item per cost...

I know that DK has a shield, but it's not a reason :)
The dragon is considered as a ranged hero so he doesn't get the damage block. And when you remove the damage block the whole point of Vanguard is gone - it's just a waste of perfectly good components that could go into way better items.
Why not just get Vitality Booster + lifesteal for sustain? Or Armlet of Mordiggian + lifesteal. Or Ogre Club for BKB. Sounds much better.

A vanguard to me is a trying not to lose item. It's one of those items that you only get if you are going full turtle.

Yet the problem is; is that you are sacrificing a trying to win item for it. Have ran over so many carries who went Vanguard in their vain hope of trying not to lose.

The big problems with Vanguard are:

1) It's basically not as good as a Mekansm
2) It's got no scaling into the late game

It's actually a really effective item early-mid game as that damage block is pretty big - however it's not so good later at all, and because you can't disassemble or upgrade it, there's nothing you can do except sell it and replace it at a considerable cost.

Drum of Endurance and Ring of Aquila are somewhat "stop gap" items to give you a stronger midgame, but they do their job well and provide team auras. Some games you really need them to stay competitive midgame, where trying to rush big late game items backfires as you don't get to complete them.

What about Vanguard for Spectre?

Never.

Spectre's early fighting power comes from Haunt, you want to beef her up with Strength, raw HP is useless as it doesn't benefit her Illusions.

no, no, it works, illusions *do* get HP bonuses. Only Meepos don't.

I still don't like Vanguard Spectre though, I made a guide on it actually.

Do illusions have the damage block?

No, they don't. Makes more sense getting an Ogre Club if you want to get tankier, as you can make it a BKB.

Then... why is Vanguard always a core on her?

It's not! The only time Spectre was picked in TI4 it was a Drum/diffusal/manta build.
Just because something is in the suggested items doesn't mean that it's good. Shadow Blade advised as core on Sniper and Drow Ranger is a typical example of horrible advice.