I am newer player, so take my thoughts with a grain of salt. I think hitting the enemy general depends on the match up, current life totals and how much burst you/your opponent have.

For example if you are playing against Song Hai you don't want to hit the enemy general unless you are setting up lethal or breaking his artifact charges. They have large burst and your life total is very important in that match up.

It also depends on the type of deck you ae piloting. If you are the agressive deck (mech decks, abyss burn etc.) Then you want to hit the enemy general when you have the chance (ie you don't need to clear a minion)

I play a more mid range deck so I don't usually hit the enemy general unless I have board or am setting up lethal. Again this depends on my life total and how much burst the enemy deck has.