I don't know, I think generally I'd tell the architect what kind of house I wanted, then ask him how much it would cost, not tell him how much I want to spend, and then find out what I can get for it.....
You have it backwards. In my previous 'analogue life' I sold home building packages for about five years. The first question you ask is how 'much money do you want to spend'. Are you seriously going to pay an architect several thousand dollars to design a house that you can't possibly afford to build? Because unlike the norm in our industry, an architect will charge for EVERYTHING.
In our case, should we spend hours of our time developing a proposal based on what clients say they want just to find they can't afford it or don't have a budget for it? If a client won't give you a budget will they cover your cost of developing this porposal as an architect would be payed for developing the blueprint for a house?
I have been very successful dealing with clients by asking how much they are thinking of spending and then working with them to prioritize/decide what they can get for that price. It's my experience that what people want and what they have a budget for are two seperate things.
Don't get me wrong, the client can give you a brief scope of work to give you an idea and we can quickly ballpark them. I'm speaking of actual esimates. It is not in your best interest to go far into that process until you have a budget.
Why are people so afraid of asking for a budget? Trust me, clients know you're going to have to ask.

Ever buy a car? What was the first criteria in your decision making process? Price. You look at your price range and then look at cars withing that price.
As mentioned above there is no use talking to a client about features like shopping carts and CMS when they can't possibly afford it.
And Ken, your strategy would not give a very good return as you hand in a price based on what the client says they want without working on the best strategy WITH them. I get a far higher conversion rate when I design a strategy based on the clients' budget.
To be honest, it's somewhat insulting that you suggest we are 'rip off artists'.
Sanity, Diane, Paul bang-on!