It appears, from the previous answers, that practices vary depending on location and company. And there's a debate (part of which you can see below) about whether it's really necessary to do an exclusive buyers's contract at all.
What I'm used to is: (1) A buyer's contract (2) Signed very early in the process, when the buyer decides on an agent to work with. But, again, as you can see, practices and opinions vary.
I'm guessing that your agent didn't want to "bind" you to a general agreement, but only saw the need for one when you identified a house on which you wanted to make an offer. And that'd be OK. I do think it would have helped if that had been discussed up front--if the agent had told you early on: "I don't require a signed agreement at this point. But when it comes time to make an offer, then we'll sign the agreement applicable to the house you're interested in." That would have avoided the surprise you ran into.
As a practical matter, from your description--that you've been working with the agent for several months--it sounds as if the agent probably earned the commission on this transaction. If you agree, then there's no harm in signing. If you disagree--let's say you found the home completely on your own--then you might consider not signing.
One other factor, though: Whether you sign or not, the house won't be any less expensive without a buyer's agent involved. The seller has already signed a listing agreement with HIS agent regarding the amount of commission. If you're thinking that you can save some money without having your own agent involved, that's incorrect. So--with or without an agent, this one or a new one--the costs to the seller are going to be the same.
Hope that helps.