You forget that the a carrier merely carries planes that are operated by the US Navy, which are the F18s.

The US Airforce is a separate branch of the military and they deploy to friendly airbases near the conflict zone. F15s, F16s, A10s, etc are all not carrier capable yet they are in use in the Middle East.

They do project a whole lot more of their air power than what can be carried on carriers alone. This is why they build a military alliance with other countries.

Russia and China lack this capability simply because most other countries will not allowed those 2 to use their bases. Note how Russia can only base their jets in the region of Syria controlled by Assad while the US can use several bases in the Middle East with the permission of their host countries.

Than there's also the US Marines, yet another separate branch of their military who also have Harrier Jump Jets on their amphibious assault ships which are as big as the carriers of other nations, but are technically not 'aircraft carriers'.

They do send a whole lot more than a mere 1%.