I live in the Netherlands. Our situation is as follows:

Mortgage interest is 4.8%. I can deduct this against 42% income tax. So I pay 0.58 * 4.8 = 2.784% myself.

But it doesn't end there. Holland has a capital tax of 1.2%, of which the first own house is exempted. Paying off the mortgage (instead of investing) saves this tax. So the effective rate of the mortgage becomes 2.784 + 1.2 = 3.984%.

But that's still not the end. Holland also has a tax on imputed rent (eigenwoningforfait). You have to add a percentage of the estimated value of your house (for a decent house this is 0.6%) to taxable income. So, for a 200k house this is €1200. Assume this is taxed by the marginal tariff of 42%. This will be €504 per year.

But of course it's not as simple as that. If your mortgage is very low, there is an exeption to the rule (wet Hillen). The imputed rent tax can't be higher then the deduction on the mortgage interest. So, as soon as you can deduct less then €504, this will decrease. In these situations, repaying the remainder will be beneficial.

Conclusion: the situation tends to be highly complex and very dependent on the fiscal regime and the interest rate that can realistically be achieved. Making sweeping statements is perilous.

If you ignore the imputed rent thing, not repaying is theoretically better when you can invest with a yield of more than 3.984%. But this implies some big assumptions:

1- that the fiscal regime stays unchanged. Here in Holland the rules change all the time. Mortgage interest deduction is under debate at the moment. No-one knows how the situation will be in 5 years time. The government can choose to index threshold numbers or not. The government can choose to change the boundaries of tax brackets. Or the tariffs of the tax brackets. Or the percentage of imputed rent tax. And the house is reappraised every year. Assuming a stable environment is skating on very thin ice.

2- here in Holland most mortgages are fixed-interest for about 10 years. Refinancing during this period is often not a good deal since the bank will levy a penalty that's close to the difference in interest. But waiting for renewal is a gamble too: no-one knows the interest rates in e.g. 5 years time. On top of that, 2 of the biggest banks here are nationalised, and a third is still on state aid. Competition on the mortgage market is virtually non-existent at this moment. So it's impossible to predict what kind of offer you will get in the future.

3- you don't know the interest rates of the future. If interest rates turn out to be in the double digits when renewal is due, you'll be very happy with a mortgage-free house.

My personal opinion is that's best to make hay while the sun shines. A low interest rate provides the cashflow that can be used to decrease gearing. When interest rates go up, free cashflow will dry up and repaying will become a lot more difficult. Call me emotional if you want.

About a mortgage as inflation-hedge. This is of course true, in theory. Because it assumes that your income will follow inflation while mortgage payments stay fixed. But for people on a salary this tends not to be the case: in situations with high inflation, salaries tend to stay behind. So, theoretically, your mortgage payments will decrease measured in purchasing power, but the purchasing power of your income will decrease too. And you will still have to buy food. In this kind of environment, fixed costs can still be a millstone, even when in theory they are shrinking. Of course, if you have the slack to survive until salaries catch up, you're laughing. But a large amount of people will be crushed in the process. Ask the Germans.