Should I pay money towards my mortgage?

We have recently moved and after selling our old house, which was paid off, have an extra 200K in savings. I was planning to put the extra money towards our new mortgage, but was advised not to since our mortgage rate is so low. The money is sitting in our savings account earning next to nothing.
• We have no debt / credit card / car…nothing (other than the mortgage)
• We have plenty of emergency money.
• We max out our retirement accounts each year.
• Max 401K and Roth
• We have a lot already invested in stocks.
• Mortgage rate is 3.5 percent / 300K mortgage.

Everywhere I read, people say to pay off your other loans first, or max out retirement…etc. We do all of that and I am not comfortable putting more into the stock market. As stated above, we have plenty invested.

So, given our situation, what investment can beat our mortgage without risking everything in the market? Should we move some/all of the money to the mortgage? Is there something else that I am missing? If the answer is 'no', then is seems no one should ever make additional principle payments. According to Dave Ramsey, pay it off. Any advice is greatly appreciated.

Thanks in advance.

Read more: Should I pay money towards my mortgage?