For the driver, the 4-level stack is the nice choice for two intersecting freeways. Each road has a direct connection to the other roadways, with no looping or weaving, and the ramps cross in a 4-level deck you can see for about a mile. If the ramps are two lanes wide, the interchange has quite high capacity and drivers with good tires probably won't even have to slow down. What's more, they're easy to navigate: there's one exit for Route Foo, on whose ramp you can later choose Foo North or Foo South.
So why aren't stacks used everywhere? The disadvantages may include geometry, materials cost, and local opposition. To raise a ramp 60 feet or more requires a lot of concrete, or fill, or both. The higher elevation of the topmost ramps requires a longer approach compared to other interchanges, which can sometimes conflict with nearby interchanges on the freeway: there might be no room to fit a stack between adjacent interchanges. Finally, towering interchanges can bring on political opposition from nearby residents who resent having a freeway's shadow receding across the front lawn every afternoon.
For example, plans for the CA 17/CA 85 interchange in Los Gatos, Calif., were modified from a multilevel structure to a low-profile cloverleaf variant to appease the neighbors.
The first four-level stack interchange was built in (surprised?) Los Angeles, around 1952. US 101 and CA 110 intersect there, and leading north is the area's first freeway, the Pasadena.
When direct HOV connections are used, they can add a fifth level to a stack interchange. The I-105 / I-110 interchange in Los Angeles includes a carpool-to-carpool connection reaching 122 feet above ground level. The FHWA Excellence in Highway Design exhibit includes a nice aerial photo of this interchange.
The flyover ramps can literally fly over: for example, ramps for the US 101 / I-280 / I-680 interchange in San Jose vault over a smaller cloverleaf interchange at 101 and Story Road.
Suppose the two levels of flyover ramps were flattened into one. The crossing traffic could be controlled with a simple two-phase signal. The interchange would have lower capacity, but would cost less.
This variant was proposed as the stacked diamond in 1985 and might see use somewhere. It's functionally a type of SPUI, but has some volleyball genes as well.