Well, your theory does not hold at all if you look at Switzerland which pollutes 1/4 of the US per capita. CO2 pollution is not and does not have to be correlated with standard of living.
If you want meaningful CO2/capita comparisons, you also have to be very careful with countries that get ("free") hydro power opportunities for electricity because that distorts the picture massively (same for e.g. Norway).
Big producers of hydrocarbons, on the other hand (like the US) have to work hard to resist the allure of cheap & convenient fossils.
Switzerland is so far ahead in this comparison because they get a lot of CO2-free hydroelectricity (>50%), have to import most hydrocarbons (=> incentive against) and also save massively on transportation because density is much higher.
Some fraction certainly is. Here is trade-adjusted CO2 per capita: https://ourworldindata.org/grapher/consumption-co2-per-capit...
Note how this still trends down for most western industrialized countries despite positive economic growth over the last two decades.