I've been doing OK at online poker without a warm fuzzy understanding of equity. I own a house, or at least the bank and I own it so I do have a notion of the term and its consequences.
To me equity is something tangible that I can retrieve fairly easy. I never want to complicate things more than necessary when retrieval is the goal. If I have equity in the pot, and I am satisfied with the amount, I DO NOT WANT IT TO GET COMPLICATED. I am not so greedy that I let that greed cause me extra complications to get satisfied. Greed kills, and unbridled greed kills with no mercy.
All that said, there are times when pushing a situation is better than floating a situation or visa
versa. Remember that those odds
are calculated using pure numerics with no consideration of the external influences of either your bets, or your opponents bets.
Given the nut flush draw on the flop example, those influences can be huge. If you hold the Ace to the nut flush draw in your hand, it is a different situation than if the Ace is on the board and you hold the King in hand. If you are first to act or are reacting to a move those equity odds are in wild fluctuation.
The temperament of your villains is a huge influence on your response.
As has been said so many times, poker is about playing the players as much as playing the cards. The effect of a raise and its sizing become huge factors in almost every hand where you are able to approximate odds. So in this example, being first to act warrants a big raise, where as reacting to a raise could easily warrant folding this situation. Same cards, same players, but NOT the same situation.
Moral of this diatribe? None, and since it is my first serious attempt of the day to seem knowledgeable it should probably be considered written by a sleepwalker......