Well, interest rate on a mortgage is 1.6% give or take.
That's more than you can currently get from a savings-account - much more.
Of course, you can invest in an ETF or whatever - but those returns are not guaranteed, as is the value of the fund itself.
Wwhile your tax-load increases as interest payments decline, it's AFAIK not prohibitively expensive to do so.
Also, when you're retired, your income will be much less and thus your tax-load.
But if you didn't pay off anything, you'll still pay interest to the bank. The bank doesn't care how much you earn.
So, if you're very conservative, paying off a mortgage actually makes sense.
(IMO): no bets on the stock-market, no bets on continuing ultra-low interest rates. That's the really risk-averse approach.
I wouldn't encourage to put literally every Rappen into paying back the mortgage.
But be advised that banks like to hand out mortgages when you're young, but after retirement, they become very strict and sometimes the bank just says "No" - and then you'll have to sell.
This is usually the case when AHV+BVK is not enough to cover the 5% rule (and no other income).
I do know a guy who took out a Libor mortgage in 2007-ish, from his employer (UBS) at very-close-to-zero % and has kept it ever since. He has paid down about half of it by now, IIRC. But I consider that a once-in-a-lifetime window of opportunity.
While it makes sense to look what other people are doing, you should ask yourself what you are ultimately comfortable with. Because if the though of the mortgage keeps you sleepless at night, what fun is the house?
;-)