According to MMT (Modern Monetary Theory) governments sell debt in the form of bonds in order to create a stable store of value for investors. They feel safer making risky investments if they know that some if their money is safe. Governments, particularly governments with fiat [1] currencies, are extremely safe borrowers. You can more or less guarantee that their bonds will be paid back. Because if a government wants to pay that bond back they are incapable of running out of money. So governments could buy their bonds back and forgive them but it would defeat their actual purpose. I read about MMT in The Deficit Myth. It's an interesting book and worth the read id you want to a different perspective on monetary theory.
Fiat in this case means the currency is not based on any asset. Common currency basing assets are gold, silver, petroleum, and cryptography.
About 22 percent of the US government’s national dept is money one department of the government owes another part.
Offhand, the majority of the government dept is in government lines and bonds. While the government can buy back its own bonds, people tend not to sell said bonds for less than their worth and so you would need more money than what it takes to just pay off the bond. Moreover, said bonds are generally low interest, and so often get smaller with inflation.
In addition, most banks, mutual funds, hedge funds, large corporations, etc... tend to have rules that say that there is only so much financial risk they can be exposed to, so if they want to make a high risk high reward bet, they need to have a certain amount of low risk of investments aswell. Government bonds are seen as about the lowest risk investments possible, and so can often be more valuable than just the money the bond itself is actually for when used as the bedrock upon which the modern risk based US financial system is built on.
Given that bonds have an limited lifespan, it’s almost always cheaper for the government to let it time out then to buy it back.
Similarly, a not insignificant part of it is in pentions. Basically when you work for the government your paycheck says you get X part of your pay now, and Y when you retire. The idea is that no matter how bad you are at managing money or if you get a bunch of medical dept or such, you have a guaranteed retirement fund. Meanwhile, from the governments perspective, thanks to inflation Y is going to be worth a lot less real money when you take it out then if they gave it to you now. Y is dept, and since the government employs a lot of people, Y is actually quite a lot of dept.
Print Money (immediate, but causes inflation and can wreck your economy if you do it too much/fast)
Sell bonds (debt) (Immediate, but need to be paid back with interest)
Bonds by default have a period (10Y, 20Y, etc) on them, after which the issuer pays the whole amount back (and they've been paying interest the entire time)
The public debt is really just a bunch of these bonds, and they're constantly cycling through. If the government doesn't want to use tax money or print money to pay them off, they just issue new bonds, and use that money to pay for the previous bonds.
Sometimes the government wants to push the debt down, so they use taxes or printed money to buy the bonds and "cancel" them. Governments don't always run deficits so this happens automatically when they have a surplus.
So to answer your original question, the reason they may not want to, is that they may want to spend the tax money elsewhere, or they may not want to deal with the problems of printing so much money regarding inflation.
It’s worth noting that a solid link between money printing and inflation has to my knowledge never been demonstrated outside of hyperinflation scenarios. The chief problem being that there are far to many inputs to inflation and deflation to solidly say how much influence some of the smaller ones like total money supply have.