Yes, but not the way you are claiming.
> Inflation is the treadmill that keeps the economy going
If by "inflation" you mean printing money, no, that is noise in the price signals that keep the economy regulated. And as central banks print more and more of it, they mask valid price signals more and more and thereby make the regulation of the economy worse and worse. And then they claim they need to print more money to "fix" the problem.
If by "inflation" you mean "prices going up", if the money supply were fixed, the prices of everything going up would signal an unhealthy economy, not a healthy one. With a fixed money supply, in the short term, whenever the supply/demand situation changes (and it is always changing), some prices will go up and some will go down. In the long term, the general price level would be expected to go down as average productivity improves. If the general price level is going up, it means average productivity is getting worse, which, as noted, is a sign of an unhealthy economy.
The main purpose of printing money is to allow governments to obfuscate the fact that they are making the economy worse by masking what would otherwise be obvious price signals showing it. Every ordinary person understands that if the prices of everything are going up, that's bad. So governments, politically, cannot allow sustained increases in the general price level, unless they are so small as to not be noticeable except over many years. But they can't micromanage their way to a healthy economy either, so their only choice is to print money to disguise what is going on.
> the obvious answer to solving unemployment is a job guarantee funded through "printing" money
This would be government micromanagement on an even more massive scale and would be a disaster.
The obvious answer to solving unemployment is to make it easier for people to start businesses, since that is what creates new jobs. The way to do that is for the government to stop micromanaging the economy and let individual people figure things out.
Well, right now they are "macromanaging" it away from a system that could possibly work. Central bank policy heavily skews toward capital and thereby into deflation (or at least lack of inflation). Inflation is the treadmill that keeps the economy going and it has been broken for a long time.
The more I get into economics the more I understand that the real world is not meaningfully different from a game in terms of policing. The details are different but general concepts like deflation or inflation are still the same. The fact that economies can only function if money is in the hands of those who are doing the work is still the same. In the most realistic economy games it is even possible to liquidate your company and start fresh after messing it up. So there is now the obvious problem that if you want a growing player base you can't just let the biggest players take over 90% of the market and force newcomers to compete with them and let almost all of them fail like in the real world. Unemployment can't exist in such a game, "unemployed" players aren't playing the game!
Well, the obvious answer to solving unemployment is a job guarantee funded through "printing" money. If people are unemployed they will take the job guarantee which in turn creates new money. Suddenly there are lots of paying consumers but since the guaranteed job doesn't actually increase the supply of goods we get to see inflation among consumer goods. Now you may be thinking that this will cause runaway inflation except it can't. When demand for products increases, so does the demand for labor. New jobs are created which pay more than the job guarantee but they don't cause inflation. It's a self balancing system.