B737: V2 = Limited manoeuvrability = 15 degrees of bank + 15 degrees turbulence upset.
V2+15 = Full manoeuvrability = 25 degrees of bank + 15 degrees turbulence upset.
Therefore <V2+15 you can use HDG SEL at 15BA and at >V2+15 you can use LNAV and >15BA.
In the old days before speed tapes & FMC bugs you used to bug V2 & some companies V2+15 as well. It saved o the mathematics under stress. Now you have a 'picture'. Below the white bug 15BA, at or above white bug >15BA. Simple and very useful under stress.
ET is flown at V2 to maximise climb performance. It is the speed the obstacle clearance & turn radius is based upon. Therefore it is flown at 15BA. It's not quite true to say it is the maximum speed you can fly an ET at. Boeing did not invent ET's. It's all to do with manoeuvre margin and bank angle.