You can, and many people do. That's actually one of the great challenges of being a web professional; convincing people what we do actually takes years of skill, research, and practice. People see services like Godaddy's Website Tonight™, Squarespace™, or Wix™ and think that web development is just dragging and dropping icons and entering in text. Clients can also receive a bit of sticker shock when they see the price tag for working with a pro web developer or designer.
The problem with the cheap website builders is customization. They look fine and great with the pre-loaded content, but the moment you drop in your logo, change the font, add in your content, or upload a picture, things...start...to look...strange. You try to adjust it yourself, but then you slowly realize you're in over your head. You don't have access to the code to make proper adjustments, and even if you did would you know what to do?
And if you do make only minor adjustments to the point where the template's integrity is still intact, how professional does your business look when it's obvious you used a $10 template builder?
Now let's think about overall website strategy. These days a company's website is a portal that all customers walk through to eventually do business with your company. There are many factors to be taken into account such as calls-to-action, conversion rate, content strategy, and overall polish and professionalism. It's typically best to leave it up to someone that knows what they're doing.
It's obviously cheaper to put a post on Craigslist to find some greasy independent 'mechanic' to replace your car brakes, but would you really want to?