core build is

He needs HP and resists to survive in a teamfight, so one armor and one MR item is necessary at a minimum.
core build is

She needs burst and safety. Gunblade provides burst for that first passive proc, and hourglass lets her survive enemy burst.
core build is

Eve needs AP to make her burst meaningful, but more importantly she needs mobility to reliably get in range to charm. Mobis and Protobelt guarantee she gets in range, while Runic destroys them.
core build is

Twitch needs hurricane's bolts to unlock his AOE potential, and then IE to make that AOE hurt. Without that, he's not really that impactful (barring, of course, a surprise mid gank with red buff at level 1).
Meanwhile... what does a
really need?
She's generally sitting further back, so excessive tank stats aren't necessary. She's got a lot of defense mechanisms built in, so something like hourglass probably isn't necessary either. Her damage doesn't need to be improved, so AD and AP are neither here nor there.
She already has everything she really needs just off her base kit. She can just build whatever the team needs.
There's a reason almost every supports core build is some variation of
.
- They need boots for obvious reasons.
- They need a GP10 item in order to afford items for the team.
- Sightstone is the best (and most efficient) team item in the game.
Everything on top of that is either a luxury or something for the team.
Yeah, some supports synnergize greatly with some items (Morg+Hourglass), but even then it's not like they aren't online before they get that item.