Is making faster military fighters even practical? I was curious after reading a book on Cold War plane development about the Soviet ideology of making increasingly powerful jets that could break Mach 3 and so on. With the advent of BVRAAM's such as the Meteor and lasers that are already being scaled down, what are the advantages to increasing the top speed or cruise speed of a fighter jet?
In the 1960, faster fighters were seen as desirable as they could outrun 1960s technology missiles to an extent (see the reports of SR-71s being fired on but never hit by SAMs). Of course, missile manufacturers saw this and developed faster missiles and longer-range radars to negate this advantage. And as it is much easier to make a missile faster than it is to make a large aircraft faster, that's an arms race the airplane manufacturers always lose. 

While high speed allows you to outrun missiles, it also reduces maneuverability: at Mach 3, a constant-G turn will be much larger than turning at the same G level at Mach 1.