I think the human mind was engineered for activity not productivity. This is why we jockey for position on roadways even though we don't get to our destination any earlier. This is part of why we are uncomfortable in elevators where we can't do anything for 30 seconds or more. This is also why people buy new websites without setting a goal for what this investment will achieve.
Call me crazy, but I think if you're going to spend money as a business, you should have a plan for how that money is going to generate more revenue. If you're going to buy office furniture, you should probably be thinking about who is going to be sitting on those chairs and how they will help your company grow. If you're hiring a new employee, you should have a job description for that person and a way to measure if that job is getting done and what it means for your organization. And if you buy a website, you should have a plan for how that is going to increase your revenue.
Your website has a job. At a minimum its job is to "answer the call" when someone enters your url into a web browser. In other words, when someone "comes to your website" your website's job is to be there for that visitor. In this regard, your website is really no different than the receptionist that greets people when they enter your office suite or answers the phone when they call. Your website receives visitors, and its job is to receive them in a way that makes your company look its best.
An ugly website can still do the job. You may be shocked to know that at least 3 of the 10 most popular websites in the US are not just unattractive, but outrageously ugly with almost overwhelmingly bad user interfaces. I am referring to the following:
These websites are not just aesthetically bad, they are horrid. No designer in his right mind would conceive of these optical monstrosities. But I think they are absolutely beautiful.
Here's why: each of these websites is amazingly good at doing its job.
Incidentally, these websites are also immensely profitable. One accounting I saw estimated Craigslist's annual profits at about $700 million per year. Not bad with a staff of 50 people and an ugly website.
Before you trash your site, ask what its job really is. If its job is to look pretty, consider what that prettiness is actually worth to your company. Then hire your design firm accordingly. Chances are, your website can do more than just be a pretty face. Think about what it can do to increase revenue and build brand loyalty. Then consider inbound marketing and SEO and hire your agency accordingly.