Paying off the house early rather than saving the money isn't a bad choice...it's just not always the best financial choice. I think if you have no other debt, there isn't any pressing economic reason to pay off your mortgage ahead of schedule. Personally I'd rather have that money more liquid and (relatively) easy to get to in times of need. For example, if something happens and you need to pull equity out of the house, you'd need to either sell the house or get a HEL or HELOC. Selling can take months or even a year (or more) and getting HEL or HELOC may not be possible if the reason you need the $$$ is because of job loss. But if that money is in a bank or investment accounts (invested in safer things like bonds if peace of mind is what you're looking for) you can pull the money out and have it in a week, and no worries if you're unemployed.
That said, often paying off the house makes some people sleep better at night, which is something that is hard to put a price tag on.
Like I said, it's not that paying off the house is a bad thing to do. There really isn't a wrong answer to this and an individual, after weighing all the options, should do what makes sense to them.