In truth, most business owners aren’t really ready to start work immediately anyway. Those few weeks of prep time before starting the actual design phase can be used proactively to work with a copywriter to solidify your content and messaging, a photographer for taking headshots or other product images, and so on. You can use those weeks effectively to have material ready for the web designer, shortening the span of time it takes to design, develop, and launch your new website.
Of course, there may be the odd time when you have a time-sensitive event coming up and you need something done in a week, and yes, there’s an advantage in an agency in this case. But for most website projects, the difference between starting work on November 1st or November 30th is often negligible to your overall business. Why not wait for the person who’s the best fit and with whom you’ll have a great working relationship for years to come?