Why do you think that a country with more taxpayers has more money for "trappings"?
"The trappings" are essentially a fixed cost at any scale of country.
Let's say you need a palace, a security detail, a motorcade, and a jet to have all of "the trappings" for the ruling family. If you assign some costs to these things, say $500k/yr for the palace, $1mm/yr for security, $500k/yr for motorcade, and $10mm/yr for the jet, you can figure out the annual cost -- $12mm/year in this example. So in a country with only 3.3 million people, that's $3.60/citizen/year for the ruling family to have their trappings. In a country with 310 million people, that would only be $0.038/citizen/year.
Even if you need more security, or a bigger motorcade, or a more expensive plane, you're still on the magnitude of pennies/person/year instead of dollars/person/year.
The size of the head of state is rather constant, and that is the only size discussed here – of course the underlying bureaucracy grows larger in larger countries, but that doesn’t mean the president can suddenly be in two jets at the same time.
Sure, the president can't. But since the size of the country is much larger, there's the governors and mayors of large cities which govern about as many people as the head of Uruguay and I'm fairly certain that each of those has a "palace" about as big as the presidential palace in Uruguay, a motorcade, a security detail larger than 2 armed guards and neither of them showed up on a vespa after elected or - for that matter - any time at all.
Let's say you need a palace, a security detail, a motorcade, and a jet to have all of "the trappings" for the ruling family. If you assign some costs to these things, say $500k/yr for the palace, $1mm/yr for security, $500k/yr for motorcade, and $10mm/yr for the jet, you can figure out the annual cost -- $12mm/year in this example. So in a country with only 3.3 million people, that's $3.60/citizen/year for the ruling family to have their trappings. In a country with 310 million people, that would only be $0.038/citizen/year.
Even if you need more security, or a bigger motorcade, or a more expensive plane, you're still on the magnitude of pennies/person/year instead of dollars/person/year.