Some topics no one has mentioned...
Taxes. Your mortgage is far too low to for the mortgage interest tax deduction to apply, you're getting the standard deduction instead, unless there are special situations (check last years return...) so this means you're paying off a 3% loan with POST tax income. The problem is some people will propose you invest to obtain, perhaps, 6% of additional marginal PRE tax income instead of paying off the loan. Extremely superficially in a tax-free world that would be a profit of 3% per year. However, my marginal total tax rate is far over 50%, so merely to break even I need to get, perhaps, 7% rate of return on a $100K investment to have enough cash left over after paying about 4% of that back in income taxes just to break even on paying a 3% $100K loan. And I'm not doing all this complicated financial shuffling for less than, say, $3K per year, which is an additional 3% return on a $100K investment, so just to make it worth my time and effort to do complicated financial shuffling vs paying it off, I need a rate of return around 10% per year on my $100K investment, which is essentially impossible.
The second issue being carefully ignored is risk. The odds of your mortgage payment being due next month and every month until you pay it off or foreclose are approximately 99.9999%. I'd give perhaps a 1 in a million chance of financial collapse or asteroid strike or nuclear war in which case you don't need to pay your monthly mortgage payment every month. The only financial investment I'm aware of with a 99.9999% or higher likelihood of on time payment every month is federal bonds. So all you need to do is find a T-bond paying somewhat over 10% per year and todays rate is ... Oh... 10 year t-bonds are running 2.98% this week. So unless T-bond rates quadruple (which would result in their own financial crisis...) then you're FAR better off paying the loan off than attempting to invest and stay ahead of the steamroller every month.
The third topic not being discussed is its VERY easy to go back in historical records and find a financial investment paying perhaps 10% with 100% odds it'll happen, because it already happened. Its VERY difficult to find something like that looking forward. If you have a crystal ball to loan me, please do so. Worse, you'll find plenty of extremely long term stats that if you invested in the stock market last century you'd get an average return of X percent blah blah even with the effects of the great depression, but your house mortgage will foreclose in mere months and the great depression lasted years. You cannot pay a monthly bill using "decade long average returns", you need that cash each and every month like clockwork or you lose the house. The financial market is very loan shark ish and responding to "Where's this month's money?" with "well on century length average I give you lots of money" is just going to get you kneecapped with a foreclosure.
Using the concepts above you're almost infinitely better off paying the loan off early rather than trying to invest in a very risky high rate scheme to generate enough marginal pre-tax income to make a profit after paying the loan with post-tax income.
Something to keep in mind is if your monthly mortgage payment is maybe $2K then when it's paid off you'll have maybe $5K/mo to invest in financial schemes per your claim. So investing $3K/mo with large amounts of debt probably won't win in the long run vs investing $5K/mo a short amount of time in the future without any debt. If the mortgage were a microscopic fraction of your total monthly investment plan then it wouldn't matter, but you could nearly double your lifetime investment rate. Sending interest money to a bank in NYC will never make you rich, you have to send investment money to a broker working for you; you want to invest in the cash cow not be the cash cow.