They cannot just print infinite number of notes
Actually, they could. Printing say 1 note for every 9 notes in existence would lead to an inflation of around 11% and is equivalent to a uniform property tax of 10%.
The reasons we don't do things that way I can think of are:
- it would make inflation huge (government spending typically is over 30% of GDP; that would give over 50% inflation)
- it was not possible under the gold standard.
- people would feel it as unjust that one's cash and bank accounts are 'taxed', but e.g. houses one owns are not.
- because of the former, it would tax the poor way more than the rich.
It would be a really good way to stimulate consumer spending, though.