Is it bad to compete with small businesses?

Don't be ridiculous. Provide value to people. That's your job as an entrepreneur (hell, as a human being...it's what sets us apart from all other animals). If that value is better than existing businesses, great, you just made the world a richer place for everyone! However, I suspect you won't find that you can just walk into an existing market and eat the existing companies lunch.

You'll be shocked at how big some "small businesses" are, and how effectively they can compete with your new-fangled web-based concept (or whatever). Most won't even notice you exist while you bang your head into the market for three years or so--if you're still in business at that point and have actually acquired a large customer base before hitting the end of your runway, then they'll notice you exist. They'll have plenty of time to respond, either getting smart, or getting out.

Ideas are funny that way...you hit the market with a great, revolutionary idea, and one of the bigger established players spots it two years later and eats your lunch with it. (First isn't a guarantee of winning, or even a good indicator of it.)

Look at it from the customer's point of view instead. Is it bad for businesses not to offer competing products and services to you?

Remember you can't put another business out of action, only customers can do that. If you provide a better product or service customers will switch to you. It's democracy in the market place.

It is good to provide customer value. If you can provide a service better and cheaper than the competition, go for it.

What if your idea will consolidate a fragmented industry and provide stiff competition to 'mom-n-pops'? Is it better if the small businesses tend to not serve the customer well?

As someone who runs a small business as my "day job", I'd say it most certainly isn't bad to compete with small businesses. :)