I'm not sure I understand the first paragraph. How is pushing early going to screw you over in the long run? I thought getting towers before your opponents granted you a significant gold advantage as well as apply more pressure on them and gain you more map control?
Depends on the lane, if you have an hard carry you can't do that because even if he gets last hit on the tower if there is no farm to take on the other lanes he will have to jungle which unless you're a nuker with low mana costs (SF) or have battlefury it's really inefficient.
Obviously in most pubs there are at least two carries (most likely one top and one bot) so you won't have any space to farm, plus if your teammates already showed that they don't know the first thing about creep equilibrium most likely they're all gonna be pushed.