I don't think people realize just how poor the F-104's maneuverability was. Or what 'boom-and-zoom' tactics really mean. It doesn't mean just pulling up into the vertical and diving back down, or flying away for 10 seconds and returning. It means you need to accelerate to high mach and very high altitude and extend away from your bandit by enough of a distance that he doesn't get a fox 2 or gunshot on you as soon as you turn around. It requires a decent amount of preparation, coordination with wingmen, high SA, and generally favorable conditions to pull off properly.
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All of this is to say that while these tactics can work, especially against older, subsonic fighters, it can be a downright headache to it pull it off properly. And that's against aircraft that should be obsolete against yours. If you are engaging MiG-21s, you will have such a disadvantage in sustained and instantaneous performance that you will need to stay above 600 knots and very high altitudes just to survive. I don't know how familiar you all are with modern dogfighting, but most merges will happen at 450-500 knots and by the time any one aircraft is in a position for a reliable kill you may be down to 200 or even lower.
"boom and zoom" is one term, but I'd prefer "fighting in the vertical" (vs. a horizontal fight, i.e., sustained turn). Barrel Roll, High Yo Yo, and Lag Displacement Roll are all examples where energy tactics, in the vertical, are used to avoid having to simply turn with an opponent. These require neither high mach nor high altitude.
These tactics do take a higher level of pilot training than simply turning hard, but the USAF has had a comfort level with them since WWII in the Pacific, in particular. When faced with the Zero, neither the US Navy nor the AAF tried to produce planes that would turn with the Japanese fighter; they wanted planes that had speed and altitude advantages that could be converted, via good tactics, into superior dogfight performance.
None of this is saying that a good turn rate isn't desirable, especially in the days of early AAM and gun fighting and an F-104 pilot that got pulled into a turning fight would be in a bad spot, but the thinking behind the F-104's design (as an F-86 successor) was solid and was vindicated in the Featherduster trials, where F-104s emerged as the superior air to air fighter vs. a variety of other US models despite poor turning performance.