I can speak to the designers side of things. Although I wouldn't handle it this way, he's probably correct. Remember, architecture and design is a service business, not a product business. There isn't really a way to tell exactly what will be necessary when providing a price. What if your plan check process requires 4 resubmittals but he only quoted you for one? What then?
I can't imagine he wouldn't give you his hourly rate, or some semblance of how he charges. By the hour or fixed fee. If he can't get to within at least 10% of what he's going to charge, you might want to find someone else. He might not know what he's doing or is scared the cost will scare you away. There are a ton of reasons.
Drafters typically charge by the hour, or by the SF. Architects are about the same but spend more time on the details / code analysis etc. etc. In our area, residential design, including structural, energy calcs, and other consultants typically land between 7% - 10% of the cost of construction.
If you don't need structural it'll be less. Maybe 4% - 6% of the construction cost. Each project is different and each project requires different things. For example in CA, you don't need a designer or architect to do homes or duplexes. Sometimes just a structural engineer. In other instances you don't even need either one.
PM me if you'd like to know more and discuss in more detail. I'd be happy to take a look.