Heyo!
I would not recommend your homepage exists at any URL other than example.com for the following reasons:
- It's web development best-practice
- Most of the links you will acquire naturally will point to example.com
- Some citations won't accept a URL with anything after the .com
- It's confusing for people
- If bots can't access your homepage at example.com, they most likely won't find your robots.txt or XML sitemap files either
I'm sure other could drum up more reasons, but the ones I've listed here should be enough to dissuade you.
You can typically fare much better by giving non-branded keywords interior pages that are specific to that topic rather than the broader homepage content. This will increase the likelihood of people finding what they're looking for and is a better way to tailor your content to your audience and to algorithms.