As for why YIG spheres are used: it basically boils down to "inductors are garbage". The phase noise of an oscillator is controlled by the Q factor of the resonance you use to set the frequency. Same with the out of band rejection of a filter. Resonators can be made from ordinary inductors and capacitors. Capacitors are not too bad: vacuum or low k dielectrics are nearly lossless. But inductors tend to be quite lossy at high frequency unless you make them out of superconductors which isn't usually convenient.
The normal solution is to use quartz crystals. The Q of their electro-mechanical modes are incredibly high which is why they make such great oscillators and filters.
The one problem with quartz crystal filters is that you can't easily tune them. You can slightly pull the frequency with an external capacitor, but you can't easily change the motional LC circuit parameters.
YIG spheres are basically the solution to that problem: a high-Q resonance that is broad-band electronically tunable.
One final touch to this -- you can still make a very nice LC oscillator (if still maybe not as low noise as you'd like, for the above reasons), that's voltage controlled using varactors, but it won't be very linear. The neat thing about YIG tuning is, it's proportional to magnetization
because physics -- so the VCO linearity is very good indeed, and little compensation or calibration is needed!
On a related note, I wonder if anyone ever tried making, say, a tunable quartz or mechanical filter, that uses a stretchy or bendy substrate as resonator, so that the dominant mode can be varied over a modest range.
In a completely different direction, there are cavity resonators with free electrons -- that's right, vacuum tubes, specifically, reflex klystrons. Apparently these are quite low noise, and are electrically variable over a modest range. The internal function is something like: an electron beam shoots towards a negatively charged reflector electrode, inside a resonator cavity. The field inside the resonator controls electron motion, transforming electron energy into resonant energy. The reflector electrode controls how soon this happens, tweaking the frequency within the bandpass range of the resonator. IIRC, a typical range is maybe 100MHz out of a 5GHz center frequency -- good in its day (a reminder that the widest bandwidth all-[conventional] tube system was probably the Tektronix 585, topping out at 100MHz baseband). Downsides include, well, all the vacuum tube stuff you need (heater power, high voltages), FM-to-AM conversion, and relatively low power output.
Tim