being in debt as a country is very different to being in debt as an individual as a country's expenditure directly correlate to its earnings. in this sense, it's unwise for a country to 'save' in the same way individuals do -- since, for example in this case if small businesses collapse causing their workers to spend less (or nothing at all) the decrease in economic activity will lower tax income to the country itself.
when it comes to the US injecting 2 trillion dollars, that's from quantitative easing which is not 'borrowed', it's just generated by the central bank of the country directly to increase liquidity. it's similar to a stock split, but for a country. The total 'value' in the economy stays the same, but the additional liquidity creates an increase in economic activity for some time which may allow investors to switch investments from short to longer term. I've seen a lot of people online who think the US had $2T lying around somewhere but it's quite the opposite.
slightly unrelated to your comment particularly but -- I wish the analysis of governments being able to spend like this from the average person wasn't either 'governments are going more into debt than they should' or 'governments have money but don't use it on their people', but 'governments have access to spending powers that individuals do not, which can massively benefit an economy in the way no other entity's spending can'.