So lets start at the top.
With respect to your pig debt analogy, there is no anthropological evidence in pre-history that that is how a village operated. If you owed 5 chickens for my pig, I know you are good for it, along with everyone else in the village. Debts did not have to be maintained.
Certainly there was barter between groups, using whatever means of equivalency for exchange, like gold, amber, etc. etc. But debt didn't really come into this since the groups were not formally linked (you have to see a group again/regularly to pay/receive debt service).
As for Graeber, note that this really starts round the agricultural revolution, particularly in the fertile crescent. It wasn't so much private debt being recorded, but debt to the temple and/or monarch. There is also the concept of the Jubilee Year, mentioned in Biblical regulations, which has been argued about by modern economists since it is anathema to modern capitalism. A Jubilee was (apart from other actions) the wiping out of debt owed. Since it was owed to the temple/monarch it was not a problem to do so, and was seen to rebalance the economy.
Next, it's nice that you now see MMT as valid, but you failed to mention a crucial aspect of the MMTers view that the government can spend freely. So instead of your statement here:
"It can, and should, just make as much as it needs and then go spend it on whatever it wants."
It is in fact:
"It can, and should, just make as much as it needs and then go spend it on whatever it *needs as long as whatever it spends it on is not resource constrained*."
MMTers are very aware of inflation, and know that the government cannot simply spend cash on things that are resource constrained. I am sure this has been pointed out to you before, but you should get a refresher from the MMTers.
Also, taxation is the way of making a fiat currency worthwhile for folks to desire. It doesn't have to 'pay' for anything (within constraints of a fiat currency that the government issues, free floating exchange rate and debts issued by the government are denominated in that currency). As such, taxation can be used to smooth high growth/low growth cycles by increasing/decreasing taxes.
Finally, the examples of the Weimar Germany (and Zimbabwe for a similar reason) is spurious. Germany had reparation debts denominated in foreign currency, along with losing the Saarland to France as a commodity (and cash) resource. Keynes recognised this and called it for what it was - a disaster in the making. For Zimbabwe, it was Mugabe's land 'reforms' that effectively wiped out a resource.