Why does not paying off a mortgage and investing instead makes sense when the quantity is vastly different?

What don't understand is, let's say have a 500k mortgage at 3%. That's a low enough rate that everybody says invest your extra money into the market to make 10%, instead of your mortgage. I understand how, if you had 500k lump sum to put into the market then it would pay off your mortgage for free and then some. But in the commonly talked about scenario, people don't have 500k to put into the market to make the 10%. They're only putting in small chunks at a time. So, is paying off 500k even at 3% not better than only putting (for example) 2k a month into the market, since it'll take you years and years to get to 500k invested?