You don't just "have an extra $4,000 a month" if you pay off your house. You lose all the money that's currently earning you 4-6%.
$4k/mon is probably a million dollar loan or so, right? Well 4-6% of a million dollars is $40,000-$60,000 per year. $3,333 - $5,000 per month.
You can just fund everything you said using the interest gained on the million dollars, while at the same time putting money towards paying off the house.
Of course, we're talking about a 2% rate. If it was 4+% then it might not be worth the risk.
1. How much are your monthly expenses?
2. How much of that is your mortgage payment?
3. If you had no payment, what would you do with that money?
Let's take an example:
1. Monthly expenses are $10,000 a month.
2. Mortgage is $4,000 a month.
3. If you had an extra $4,000 a month, you could work part time and volunteer more at that coding camp.
3. Because you have $80,000 saved, you could take a 6 month road trip, and still have time to find another job.
3. You could use that for one of the 15 side projects you've been thinking of.
3. You could go on a fancy vacation every year with your family.
3. All the while, no bank can evict you from your house, because you fully own it.
Are any of those things really worth foregoing extra 4-6% rate of return? For many people, they are. All it takes is no payments.