The money burn isn't really an argument. The French republican system costs about 100 million euros a year to support. The Spanish monarchy around 9 million. Technically the British parliamentary system is older then the US.
It is a good argument. You're comparing the cost of the french republican system with the costs for the spanish monarchy but you completely forget to mention that spain also has a republican democratic system they have to pay for. The 9 million spain spends on the monarchy are mostly redundant costs. In a republic the president fulfills all the roles the monarch normally would have without spending money on useless things like royal marriages and the royal family in general. Also most royal families acquired huge amounts of money and properties throughout the centuries, when a monarchy gets abolished most of these money and properties go directly to the state.
I said democracy in the modern sense, at the time of Declaration of Independence only a very small amount of people in the UK could actually vote for the british parliament and until 1911 the house of Lords, a parliament consisting of unelected aristocrats, had a significant amount of power in the government. If you call the UK a democracy in 1776 you could as well call the holy roman empire a democracy because the emperor was elected by the seven Prince-electors.