How late in the game are we talking? After Blitz has his gp10 items and his boots and buying 10 wards every time he goes back, where does he get the money to build beefy bruiser? I mean, eventually he will have that much gold, but most games don't go that long. If they do, every support should build some damage and survivability. Soraka buys some AP for Starcall spamming and bigger heals, for example.
The key with supports is that while having AP or tank or whatever else on them is fine, they can do great without them. Soraka still has a huge armor buff, heals, a silence, and stacking mr reduction. Taric has his auras and a stun, Blitz has his hook, Nunu has Blood Boil and snowball. Supports are supports because they don't need items to work, items are just icing on the cake.
In short, of course late game you want some items to make your champion have a stronger presence. If you can do that with aura items, that's pretty awesome. If you want to grab an item or two for yourself, that's fine too, as long as you are still buying a million wards. 'Support' isn't a thing that ends at laning- it shifts from keep the carry alive/feed carry kills to keep the entire team alive/feed entire team kills. It goes from warding against ganks and playing the the proper mix of aggression and passivity in lane to warding the entire map, keeping track of timers, keeping track of the enemy team, following around whoever is most important to help them out in case they get ganked or to make ganks less likely. A good Support player takes on even more supporting responsibly as the game goes on.