If maximum speed was a priority for modern military fighter jets and bombers, approximately how fast would they likely be? Burt Rutan talks rather passionately about the lack of innovation in space flight, but also mentions how fighter jet (maximum) speed performance has stalled:


                
            

In fact, from what little I know regarding fifth generation fighters, not only has the maximum speed stagnated, but it is degrading.

Traits such as stealth prohibit variable intake geometry and variable wing geometry, the maximum speed appears to never be used in reality, it is probably costly and creates other problems (we only have to look at the SR-71 here). Furthermore, other engine characteristics are probably more desirable, such as supercruise and good acceleration in the range where this is critical and actually useful.

However, in this question I'm asking what, approximately (mach 4, 5, 6?) would the maximum speed likely be, if maximum speed was allocated a similar budget and priority akin to that during the cold war era?

The reason I feel this question can be answered at all, is that I imagine there are some very real, practical problems with very high performance aircraft that require extraordinary solutions to overcome. An answer that identifies where these approximately are would thus go a long way towards a satisfactory answer.

Basically, the crux of this question is to identify if there have been any significant aerodynamic, engine, or other performance related advancements that would enable a fighter jet to travel significantly faster than e.g. the F-15 or MiG-25, while still retaining the same functionality as namely the same types of aircraft.

Similarly for a bomber, it is well-known that sustained mach 3 flight can be achieved by looking at e.g. the XB-70 or SR-71. Even with designs from the 1950s. What is realistic today?

Just to be clear: I'm not expecting an exact figure here, but if there are any studies that have looked into this, it would be a very interesting read. If there are no studies, perhaps someone would want to take the challenge and offer a somewhat comprehensive answer as a conjecture anyway. Any math/physics would be great.

I assume that in order to even begin to answer this question, it must be defined what a "fighter jet" is, must it have an air breathing engine, or can it also have a rocket engine, akin to the X-15? Since I'm asking the question, I will also take the liberty to arbitrarily define this here: The engine type is irrelevant, there may be more than one engine, of different types, of the same type. Whatever would make sense in the context of a fighter jet, or even a bomber. Furthermore, it must be a manned aircraft. If it can reach suborbital flight and beyond, like the X-15, it is still an aircraft (again, arbitrarily defined).

An answer that separates the air breathing and rocket engines as two different categories is fine.

This definition of making if fighter jet/bomber is mostly based on wanting to exclude unmanned experimental aircraft, even if hypersonic aircraft such as the X-43 probably serve as a good reference, I feel they have little root in reality, having no life support, no weapon systems, and perhaps no practical purpose whatsoever beyond data recording.

It may also seem like a pointless question, but this might be quite useful in terms of bridging the gap between aircraft and spacecraft, or any other application one might think of -- suborbital passenger jets, etc.
Increasing the speed of an aircraft results in having to make trade-offs. Drag will increase as the square of the velocity, meaning a doubling of speed will take 4x the power to achieve. This problem is compounded by the fact that it is very difficult to design an engine (and an airframe) that performs really well at super sonic speeds, while still performing well at subsonic speeds. 

All design decisions always end up in trade-offs. Increasing maneuverability generally requires doing things that will increase the drag, which means you will require more power to compensate (which then requires a larger engine, which will reduce your maneuverability due to the increased weight). 

All of these decisions mean that, in the end, increasing the speed of a fighter inevitably requires the reduction of something else, either turning speed, or weapon payload, or range. While better technology has given us more powerful engines, and new materials and alloys allow us to create more maneuverable aircraft, we've actually seen the top speeds of aircraft go down compared to past fighter aircraft, even though we could create an aircraft as fast as anything from the past, with increased maneuverability and weapon payload in comparison. 

These decisions are being made because by reducing the top speed of aircraft, they in return also get better maneuverability, so it's conscious decision to take the higher weapons payload, increased range, and higher maneuverability in place of a higher top speed because a very fast top speed is just not all that useful in warfare compared to everything else. Reconnaissance (which is what the SR-71 was designed for) is better handled by satellites, which can't be shot down in practice, and don't require flying over another country's airspace in a way that is likely to draw their ire. Bombers would rather carry a larger payload, and be fast enough to get to the target, but getting their significantly faster at the cost of a reduced payload won't buy you much. Same goes for fighters, they need to fly around somewhat quickly, but a pure speed advantage over an opponent isn't all that useful either (compared to just having a better fighter). So it's a combination of both physics and specifically what things the military values that just means that there's little value to purely increasing speed.