What you feel is not important. You are describing an economics concept incorrectly, which will only serve to mislead students. I explained in your other comment below why this is wrong on the surface.

But your explanation of why a firm will operate with zero profit is not complete either. Most mom and pop businesses as you describe, in fact, make very little if any "profit", in fact a large percentage fail in the first few years. But they can continue to operate for a long time with zero profit because the owners still pay themselves a salary, their employees receive salary, and there they are building value in their business. Many business owners will keep a business going when their opportunity costs are higher than if they went to work for an employer, simply because they like working for themselves.

You explained the concept of opportunity cost. Fine. But opportunity cost explains why we all make decisions about many things every day of our lives, it is not just about business decisions. And it is not an explanation of the economic term zero economic profits.