Does paying off your mortgage fast really pay off?

There is a financial concern that I have noticed related to trying to pay your mortgage off as fast as possible.  Most people with mortgages are attempting to quickly pay the mortgage off as fast as possible to save money in the end by decreasing the interest accrued.  The banks also really urge people with mortgages to put any extra money directly toward the mortgage to pay it off  quickly.  That makes obvious sense to almost anybody.  However, I have noticed that you may actually be harming yourself financially by trying to pay the mortgage off as quick as possible.  Wouldn’t you be better off making your minimum mortgage payment and then put any extra money into an interest bearing savings account and letting it grow there?  I believe this might actually increase your net worth.

Think about it, you get a loan for your mortgage, which contributes to your net worth the entire value of the home REGARDLESS of how much money you put down or have paid on the home so far.  So, if you are putting your extra money into an interest bearing account instead of toward the mortgage, that money can be added to your net worth on top of the home value.  An example, you buy a home for $300,000 and put the minimum down payment and make monthly minimum mortgage payments, you have increased your net worth to $300,000.  Now the interest bearing checking account, where you are putting all of the extra money you would be adding to the mortgage is earning money in the form of interest.  Now fast forward 10 years, you have earned interest for 10 years on the extra money you would have put into the mortgage , so you have that to add to your net worth and you still have and are current on the $300,000 house.  If you had just been throwing that extra money on the mortgage for the last 10 years, your net worth would only be the $300,000.   Even if you had paid the home off almost entirely and needed some money for an emergency, you do not necessarily just get it from the bank.  Equity is given from banks on mortgages when the owner can demonstrate an ability to pay the equity back.  So, most emergencies considered, who can prove that they can repay during those times?  Wouldn’t you also be better off being able to just go to the bank and access YOUR EXTRA MONEY from your interest bearing savings account in the event of an emergency?  Why give the bank all the control, even if you are the perfect model mortgage payment maker, the bank can tell you NO to access equity.  Keep your money, increase your net worth, and have more control over YOUR CASH.