Why aren't there many level 3's in the US?
Let's check the IATA criteria:
A Level 3 airport is one where:
a) Demand for airport infrastructure significantly exceeds the airport’s capacity
during the relevant period;
b) Expansion of airport infrastructure to meet demand is not possible in the
c) Attempts to resolve the problem through voluntary schedule adjustments
have failed or are ineffective; and
d) As a result, a process of slot allocation is required whereby it is necessary
for all airlines and other aircraft operators to have a slot allocated by a
coordinator in order to arrive or depart at the airport during the periods when
slot allocation occurs.
a) Demand exceeding capacity
According to this study, the demand levels on US airports is lower compared to the EU.
In 2014 the average payload at 11 of the largest US airports was 108 passengers per
aircraft. At 10 of the largest EU airports, the average was 134 passengers per aircraft.
This confirms that the structure of traffic is quite different.
b) Infrastructure and expansion
In the US, say apart from New York, expansion is easy. A good comparison would be comparing a major European city with a major US city. The US had the benefit of hindsight when they planned for their cities. Heathrow has been trying to expand since forever, and only recently a third runway was approved.
According to this MIT presentation, for the top 34 airports, the US has 4.12 runways per airport, compared to 2.47 in Europe.
How do airlines manage?
Since a) and b) are usually not met, c) and d) are less likely to happen.
c) and d) Schedule adjustments and slot allocation
14 CFR Part 93. The FAA stepped in a long time ago, and hasn't changed a thing since the deregulation act. All the majors who had all the slots, are hanging on to them.
Any trading that happens is not through an open auction. Only once was an experimental free-market auction held in 1982. So any problem, is evidently usually solved voluntarily.
According to the same MIT presentation, when slots exist in the US, they are "set with reference to VMC capacities". While Europe uses IFR procedures figures. This allows the US to declare higher capacities than Europe. So, it's easier for airlines to schedule flights in the US.
How does it impact the pilots (flights)?
Again, from the MIT presentation, the US faces high delays when IMC (instrument meteorological conditions) sets in, because of using VMC (visual meteorological conditions) capacities. Europe is more reliable in this area. So a pilot flying into a level 2 airport in bad weather in the US is likey to be delayed, whether in the air or on ground.
Schedule reliability is much lower in the US than in Europe
Reliability of schedules in US declines over the course of a day, particularly in the presence of poor weather
In defense, US airlines have been increasing (up to 2007) the advertised flight durations; European airlines have not
European airports place a premium on predictability and "smoothing" operations, relying on (often too low) declared capacities and IFR separations at all times
They also mention delays are not necessarily due to over capacity. My interpretation: You can have a time like Christmas with many flyers and bad winter weather causing many delays and cancelled flights. But still, airlines can't apply the level 3 options. Especially that they can't resort to c) and d) to move Christmas time to the summer.
All airlines suffer, the passengers expect it, and that's it. However, there are studies for and against changing the way the US handles capacities and slots (messy debates).
So, there are two systems, with no clear winner.