That "check" makes no sense, because it acts as a throttle on the economy. It causes unemployment, which costs magnitudes more economically speaking than inflation (to which there is a ready solution). Moreover, given that the government will deficit spend (and will have to deficit spend in order to grow the economy), the effect of such a "check" is only to increase spending even further. That is because all this "check" really does is require that the government run a national bank (spending program) that grows in size anytime the government deficit spends by the amount of the deficit spending. So not only is the government spending the deficit amount directly, it is on top of that paying interest on that exact amount to people who deposit in the national bank it is required to maintain. So this "check" is a pretty shit check on spending, given that it is a rule requiring the government to increase spending.
It is not unnecessary. See: Weimer Republic.
The bolded sound like contradictory statements. One one hand you argue it causes unemployment but on the other hand you argue it increases spending (which would decrease unemployment). The statements cannot work together. And I don't see how it's possible to believe governments spend more money when they have to tax + borrow to balance their books versus create money with no stipulations.
Interest is the price of money, especially at the government bond level (which is considered risk-free). By the gov't borrowing, it is committing to more spending in the future, but it's also setting the spending rate to its best approximation of inflation. Meaning that if it is always correct, it's not spending any extra money because the money its paying back is devalued. In some cases, it pays back less money than it brought in, adjusted for inflation.
Moreover, if politicians, economists, and economic elites wish to talk about the national bank in these terms, I welcome them doing so. At least they would be being honest instead of pretending that the government's debt is financially problematic and they would be exposed for people whose position ultimately boils down to limiting government spending for the purpose of increasing employer bargaining power and suppressing wages.
It can be problematic because of the system we've designed. Sure, we can change the system, but we haven't and probably shouldn't (in a general sense). In our system the debt can be problematic under the right conditions so to say that people are pretending isn't really correct. If people stop lending to the government, it's a problem within the system. We can then change the system, but money is nothing but a medium of exchange whose value entirely lies in our minds (whether it's fiat or commodity, this holds true) and that matters.
That said, I do agree that we have a too little spending problem right now (or at the very least, intelligent spending) during a down economy and that the notion of debt/deficit being and issue is stupid. Especially given that borrowing is cheaper now that ever...