Printing money should increase inflation, yet we don't see that in the recent years in the US.
Huh?

https://www.inflationtool.com/us-dollar

$100 is 2018 is today worth $105.73

And if there is inflation, it means it takes care of the national debt
This assumes inflation is above interest rates. That isn't the case, not by a long shot. Hyperinflation might have this effect, but the downside of that will be far more damaging than manageable national debt.

I don't think inflation is a good thing. When governments print money, they are reducing the value of everyone's savings. It's basically a stealth tax. Of course, quantitative easing isn't the only driver of inflation. Increasing wages, in particular an increase in the minimum wage, causes an increase in business costs, which they then pass on to the consumer in the form of increased prices. In this latter case, assuming increased revenue from higher prices exactly matches the increase in salary costs, then nobody has lost or gained anything, it's not a tax. But in the case of quantitative easing, that's essentially theft. They're taking money from savers.