But Dr is only really good if you can use it early to kill Estates and Coppers (or you have excess actions and some way to monitor your deck).
But why do you say that? Why is killing Estates and Coppers early so much better than killing them on turn 5 to 8? Usually you want the strong trasher early because it's easier to line up your trasher with your junk. You sacrifice early economy for that trashing. But with Doctor you have the opportunity to get the early economy and make up the strong trashing after the fact. It seems to me that could very well be worth $8 or $9.
With most other trashers, much of the early game economic sacrifice comes in the fact that you have to give up a buy every time you want to trash. Since Doctor doesn't trash from hand, you don't get that with Doctor; you can keep buying Silvers or whatever while doing the trashing. Not sure that that's enough to make it substantially better than trashing via the overpay, but it's certainly a factor to consider.
Over-paying for Dr is good I guess, but then it's a trade off for other cards. Most useful if it's a weak kingdom I guess?
It would be good with a slog where you have a bunch of curses to get rid of, but when are you going to draw $8 on a slog like that and want an over-paid Dr over a Province?
I don't think it's great in a slog. I think it's better when you get an early $8 hand in an engine-ish game. Usually you don't want a turn 5 Province. Would you rather have a Gold or would you rather trash about 4 bad cards? I'm sure the answer is "it depends", but it seems to me you'd take the trashing pretty often.
If you know you're going to hit $8 by turn 5, then by all means, wait until then to trash via the overpay. I think people prefer to open with Doctor because they have no idea how things are going to turn out that far into the game, and they would rather have the more reliable early trashing than try to get lucky for a good early overpay. This may not always be the right call, but I think in most cases it's probably safer. Often times at $6, Gold is better than an overpaid Doctor; at $7, it's probably pretty close; and then maybe at $8 Doctor is better. But since you don't know whether you'll be hitting $8 any time soon, I would think it is best to play it safe.
Then again, I haven't played much Guilds, so that's mostly speculation rather than experience.
Edit: Actually I'm sure those price points depend too much on the board to say anything useful about when Doctor is preferable to Gold...