While you are technically correct about the metal fuels as propellents, if liquid hydrogen is also being injected into the combustion, then the most important factor becomes the heat produced from the fuel.
The weight contribution from liquid hydrogen is very negligable, and for large scales, this also includes the storage tank for the cryogenic liquid.
The reaction between Beryllium and oxygen, with liquid hydrogen present, has a higher specific impulse than
liquid hydrogen burning with oxygen. The highest specific impulse for a chemical propellant ever tested in a rocket engine was lithium, fluorine, and hydrogen (a tripropellant), which gave a value of 542 seconds (5320 m/s).
Methyl hyrazines actually haver lower specific impulse values than plain hydrocarbons, such as kerosene.
The reason that hydrazines are used is because they are hypergolic with N2O4 or HNO3. Hydroxylamine compounds, which are very reactive reducing agents and have much lower toxicity then hydrazine, could potentially replace hydrazine as a hypergolic fuel. For example, N,O-diethyl-hydroxylamine is a liquid. While hydroxylamine itself has an explosion hazard, many of its derivitives have no danger.
While it is quite understandable that ozone, and fluorine, boron-based compounds were abandoned, in my opinion
these fuels should still be regarded as potentially valuable for the upper stages of rockets.
Because of the risk of explosion ozone might b more suitable for use to send up low value objects, such as reserve fuel, into space. Even using a fuel combination with only a slightly higher specific impulse can allow significant cost savings. It requires fuel to lift unburnt fuel, so more energetic fuel can lead to exponential weight reductions.
If I remember correctly, using a fuel that is 15% more energetic can potentially reduce the required fuel by 50%. Considering how expensive it is to lift weight towards space, small weight savings could easily be worth the extra complexities and hazards associated with exotic fuels. Of course, for the non-professional experimenter, the gains would be very insignificant compared to the added difficulty and danger.
At present, azetidines are too difficult and expensive to produce to be suitable for large scale rocket use.
It is unfortunate that fluorine-based oxidizers tend to produce toxic HF in their exhaust. This is the main reason why fluorine oxidizers are not used. One note to mention. The US navy has experimented with SF6 burning with metalic lithium to propel torpedoes. SF6 is unusually inert, and when mixed with oxygen, it is even safe to breathe. If the fuel consists only of a metal, the metal fluorides, while still creating a hazardous smoke, are far less toxic than HF gas. There has already been much experimentation with oxygen and nitrous oxide burning solid HTPB or even blocks of wax. These have the advantage of the fuel having little danger of combustion during storage, and such engines have been proposed for future commercial use. I would think that liquid pressurized SF6 could be used to burn an aluminum core. I am not sure if this would be more energetic than nitrous oxide burning with methane, but this combination could potentially be very energetic. SF6 and Al would both be extremely safe (compared to other oxidizers and fuels) before combustion. Ideally the combustion products would form only sulfur and AlF3, which is not extremely toxic. Aluminum trifluoride has a surprisingly low heat of formation, which should not be surprising, considering the high 1291°C melting point of the compound.
"The Enthalpy of Formation and Entropy of Aluminum(I) Fluoride(g)" Hon Chung Ko, Michael A. Greenbaum, Jay A. Blauer, Milton Farber. J. Phys. Chem., 1965, 69 (7), p 2311–2316 (1965)
There would, unfortunately, also be traces of toxic SF4 produced during combustion that would inevitably escape into the exhaust
I agree, methane would be a very conventient fuel, with good specific impulse, and not extremely difficult for storage.