Why go late?

So I have been wondering why would anyone go to late game? Late game being 40+ mins.

Well if you have hard carries they excel in lategame

yeah so why not get heroes with strong early game/pushing potential? Why would people deliberately prolong the game thereby giving the enemy the chance to win?

Maybe this shows my lack of knowledge of the game, but I just don't see why I need to pay 4v6 while my spectre farms up so she can come online after 40 mins?

If I am against a team with an AM or PA or Spec, I tell my team we need to be agressive, push hard and end before 40 mins...and you know what? that happens nearly all the time.

You know what happens when MY team picks hard carries? I need to hold out until they single handily carry the team to victory.....why? Again this may show my ignorance, but I will NOT let some self absorbed hard carry take ALL the farm only to not be useful until late game, and then take ALL the credit for winning.

so can someone tell me why hard carries are even an option when your team can pick pushers, deathballers, team fighters and supports that can end the game before hard carries are even useful?