The cone inlet design can be seen on the F-104 Starfighter and the SR71 Blackbird which were both Kelly Johnson projects. Also on the F1 mirage, Mig21, and so.
I understand that they were used to weaken shockwaves, but they don't seem so popular with 4th and 5th gen fighter aircraft.
TLDR: Spike intakes were used when top speed was the most important goal in fighter design. They perform worse versus ramp intakes at subsonic speed and when maneuvering. Since the emphasis shifted to the latter, spike intakes became less attractive.
The central spike is characterized by:
Its disadvantages are:
When each new generation of fighters was designed to be faster than the last, the spike intake was the best solution. However, with the experience of the Sixties and Seventies it became clear that a conflict when much time is spent at Mach 2 will not happen. Instead, maneuverability at high subsonic speed became the design driver, initially without giving up the Mach 2+ capability (late Sixties and early Seventies - F14, F15, Su-27, MiG-29), so rectangular intakes with moveable ramps replaced spike intakes. Later, even the Mach 2 capability was dropped (since the late Seventies - F5, F16, F18, Rafale) and simple pitot intakes took over. Better simulation also helped to understand intake flows better and optimize performance: Both the F16 and Rafale intakes are placed such that at high angle of attack the airplane structure helps to get more and better pre-compressed air to the intake, a clear advantage over a central spike intake at speeds up to Mach 1.6.
All high speed supersonic inlets are designed to control and shape the shock waves.
Slower supersonic aircraft -- like the F-16, have a pitot inlet. This forms a single normal shock in front of the inlet.
As you go faster, you use multiple shocks (the final shock is always a normal shock). First, one external oblique shock followed by the normal. This is an external compression inlet.
Then, you go to multiple external shocks before the normal.
Then, you use both external and internal shocks. This is a mixed compression inlet.
Each of these stages has an increase in complexity. In order to get these inlets to work across a range of Mach numbers, they need a series of movable ramps that must be controlled. They often involve boundary layer suction to prevent massive separation in the inlet. Consequently, increasing the top speed required of the aircraft drives complexity and cost of the inlet system.
When designing the shock system, you can have a 2D system or an axisymmetric system. The 2D system uses 2D oblique shocks (ramps) to form the inlet -- this is what you see in a F-15, F-14, and most of the aircraft you mention. The axisymmetric system uses conical shocks to form the inlet.
For the most part, you can achieve similar performance with a 2D or axisymmetric system. The choice is more about how it integrates with the rest of the aircraft.
The axisymmetric system has less design freedom -- for example, you can't tuck an axisymmetric inlet under a wing.
The design of the latest generation of fighters is dominated by stealth considerations -- so if you're asking why they look different from previous generations, the answer is almost always stealth.
It would seem that integrating a 2D inlet into a stealthy configuration is easier than doing so with an axisymmetric inlet.
