seigniorage is also referred to as an inflation tax [...] the "inflation tax" is paid by those who hold the existing currency, which results from their holdings of currency becoming devalued through inflation because of the introduction of additional money supply.
That's a fair point to make in relation to a loan that must be repaid. But actual government debt has to be backed by a claim to someone's labour and that someone is the tax payer. If there is no such backing all that fiat money will quickly lose its value.