The whole thing is under the premise that you are going for a FG rush. There are plenty of strategies that just beat FG rushes period. Ambassador+village and an enginey thing is one of them. However when it comes to FG rushes, my claim is that doctor is just about as good support as you can get, especially if you hit 4 or 5 on turn 1. In a FG rush you do ignore 7-8 of the kingdom cards, and if some of them aren't ignorable, you shouldn't go for a FG rush.
It is better than chapel, steward, masquerade, or ambassador when it comes to a FG rush. That's because it is faster than all of those while still managing to buy a FG every turn. The reason it is faster is that 1) It begins trashing in the first two turns and 2) It cycles extremely quickly, and so you will see it more often. Those other 4 cards are also support for FG, but doctor is just better support than all 4. I look at these cards in a vacuum because if I don't look at in a vacuum then a FG rush is not the way to go.
When it comes to other support cards like storeroom or remodel, I am not sure if doctor is better or not, but my instinct says that if you get 4 or 5 on turn 1 then it is. See my sample game for how fast it can be.
In the end, FG rushes are a big money strategy, where you just buy fool's gold, no more than a couple actions, and green. Big money is quite often completely outclassed by any sort of engine. But when it comes to big money, I would consider doctor/FG to be one of the best.